diff --git a/site/docs/supported-models/_components/llm-models-table/models.ts b/site/docs/supported-models/_components/llm-models-table/models.ts
index 1a542e2ca4..01113a4cc4 100644
--- a/site/docs/supported-models/_components/llm-models-table/models.ts
+++ b/site/docs/supported-models/_components/llm-models-table/models.ts
@@ -229,6 +229,21 @@ export const LLM_MODELS: LLMModelType[] = [
       },
     ],
   },
+  {
+    architecture: 'FalconH1ForCausalLM',
+    models: [
+      {
+        name: 'Falcon-H1',
+        links: [
+          'https://huggingface.co/tiiuae/Falcon-H1-0.5B-Instruct',
+          'https://huggingface.co/tiiuae/Falcon-H1-0.5B-Base',
+          'https://huggingface.co/tiiuae/Falcon-H1-1.5B-Instruct',
+          'https://huggingface.co/tiiuae/Falcon-H1-3B-Instruct',
+          'https://huggingface.co/tiiuae/Falcon-H1-7B-Instruct',
+        ],
+      },
+    ],
+  },
   {
     architecture: 'GemmaForCausalLM',
     models: [
diff --git a/src/cpp/src/llm/pipeline.cpp b/src/cpp/src/llm/pipeline.cpp
index 4f9ba7dd5a..ccbbe0d199 100644
--- a/src/cpp/src/llm/pipeline.cpp
+++ b/src/cpp/src/llm/pipeline.cpp
@@ -259,7 +259,20 @@ ov::genai::LLMPipeline::LLMPipeline(
     } else if (utils::explicitly_requires_paged_attention(user_properties)) {
         // If CB is invoked explicitly, create CB adapter as is and re-throw in case if internal issues
         auto [device_properties, scheduler_config] = utils::extract_scheduler_config(properties, utils::get_latency_oriented_scheduler_config());
-        m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config, models_path);
+        try {
+            m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config, models_path);
+        } catch (const ov::Exception& exception) {
+            // Hybrid Mamba/attention models (e.g. Falcon-H1) cannot be converted to PagedAttention: their recurrent
+            // state leaves a dangling beam_idx parameter. PagedAttention cannot be honored for such models, so fall
+            // back to the stateful backend instead of surfacing the low-level failure.
+            if (!utils::is_paged_attention_model_construction_failure(exception)) {
+                throw;
+            }
+            log_paged_attention_fallback(exception);
+            // Drop any scheduler_config so the stateful backend does not forward a PagedAttention-only property.
+            properties.erase(ov::genai::scheduler_config.name());
+            model = utils::read_model(models_path, properties);
+        }
     } else if (attention_backend == PA_BACKEND) {
         try {
             // we need use CB only for x86 and arm64, as for other architectures like risc-v we can create Paged Attention based model
@@ -304,7 +317,20 @@ ov::genai::LLMPipeline::LLMPipeline(
     } else if (utils::explicitly_requires_paged_attention(user_properties)) {
         // If CB is invoked explicitly, create CB adapter as is and re-throw in case if internal issues
         auto [device_properties, scheduler_config] = utils::extract_scheduler_config(properties, utils::get_latency_oriented_scheduler_config());
-        m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config, models_path);
+        try {
+            m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config, models_path);
+        } catch (const ov::Exception& exception) {
+            // Hybrid Mamba/attention models (e.g. Falcon-H1) cannot be converted to PagedAttention: their recurrent
+            // state leaves a dangling beam_idx parameter. PagedAttention cannot be honored for such models, so fall
+            // back to the stateful backend instead of surfacing the low-level failure.
+            if (!utils::is_paged_attention_model_construction_failure(exception)) {
+                throw;
+            }
+            log_paged_attention_fallback(exception);
+            // Drop any scheduler_config so the stateful backend does not forward a PagedAttention-only property.
+            properties.erase(ov::genai::scheduler_config.name());
+            model = utils::read_model(models_path, properties);
+        }
     } else if (attention_backend == PA_BACKEND) {
         // try to call CB adapter one more time, but with safe guard to silent exception
         try {
@@ -355,7 +381,20 @@ ov::genai::LLMPipeline::LLMPipeline(
     } else if (utils::explicitly_requires_paged_attention(user_properties)) {
         // If CB is invoked explicitly, create CB adapter as is and re-throw in case if internal issues
         auto [device_properties, scheduler_config] = utils::extract_scheduler_config(properties, utils::get_latency_oriented_scheduler_config());
-        m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config);
+        try {
+            m_pimpl = std::make_unique<ContinuousBatchingAdapter>(model, tokenizer, scheduler_config, device, device_properties, generation_config);
+        } catch (const ov::Exception& exception) {
+            // Hybrid Mamba/attention models (e.g. Falcon-H1) cannot be converted to PagedAttention: their recurrent
+            // state leaves a dangling beam_idx parameter. PagedAttention cannot be honored for such models, so fall
+            // back to the stateful backend instead of surfacing the low-level failure.
+            if (!utils::is_paged_attention_model_construction_failure(exception)) {
+                throw;
+            }
+            log_paged_attention_fallback(exception);
+            // Drop any scheduler_config so the stateful backend does not forward a PagedAttention-only property.
+            properties.erase(ov::genai::scheduler_config.name());
+            model = utils::singleton_core().read_model(model_str, weights_tensor);
+        }
     } else if (attention_backend == PA_BACKEND) {
         // try to call CB adapter one more time, but with safe guard to silent exception
         try {
diff --git a/src/cpp/src/utils.cpp b/src/cpp/src/utils.cpp
index 387455d549..88c181f871 100644
--- a/src/cpp/src/utils.cpp
+++ b/src/cpp/src/utils.cpp
@@ -934,6 +934,20 @@ std::pair<ov::AnyMap, std::string> extract_attention_backend(const ov::AnyMap& e
     return {properties, attention_backend};
 };
 
+bool is_paged_attention_model_construction_failure(const ov::Exception& exception) {
+    const std::string message = exception.what();
+    // The SDPAToPagedAttention transformation fails to convert hybrid Mamba/attention models (e.g. Falcon-H1):
+    // the recurrent convolution/SSM state keeps referencing the beam_idx parameter after the parameter itself is
+    // removed, which ov::Model validation reports as an undeclared/unregistered beam_idx parameter. Match this
+    // specific model-construction failure so only genuinely PagedAttention-incompatible models fall back to the
+    // stateful backend, while models that merely hit a transient runtime error still surface it.
+    const bool references_beam_idx = message.find("beam_idx") != std::string::npos;
+    const bool undeclared_parameter =
+        message.find("undeclared parameters") != std::string::npos ||
+        message.find("unregistered_parameters") != std::string::npos;
+    return references_beam_idx && undeclared_parameter;
+}
+
 ExtensionList extract_extensions(ov::AnyMap& properties) {
     auto it = properties.find(EXTENSIONS_ARG_NAME);
     ExtensionList extensions = {};
diff --git a/src/cpp/src/utils.hpp b/src/cpp/src/utils.hpp
index 89a64b352c..446a9a23b1 100644
--- a/src/cpp/src/utils.hpp
+++ b/src/cpp/src/utils.hpp
@@ -351,6 +351,21 @@ bool explicitly_requires_paged_attention(const ov::AnyMap& properties, bool is_n
 
 std::pair<ov::AnyMap, std::string> extract_attention_backend(const ov::AnyMap& external_properties, bool is_npu_requested = false);
 
+/**
+ * @brief Detects whether an exception raised while constructing a PagedAttention/ContinuousBatching pipeline
+ *        indicates that the model cannot be converted to PagedAttention at all.
+ *
+ * Hybrid architectures such as Falcon-H1 (Mamba/SSM mixed with attention) carry recurrent convolution/SSM state
+ * that the SDPAToPagedAttention transformation cannot rewrite. The recurrent state keeps referencing the model's
+ * beam_idx parameter, which the transformation removes, producing an "undeclared parameter beam_idx" model
+ * validation failure. Such models can only run with the stateful backend, so the pipeline should fall back to it
+ * instead of surfacing the low-level failure.
+ *
+ * @param exception The exception thrown during PagedAttention pipeline construction.
+ * @return true if the failure is a PagedAttention model-construction incompatibility that warrants a stateful fallback.
+ */
+bool is_paged_attention_model_construction_failure(const ov::Exception& exception);
+
 /**
  * @brief Extracts the "extensions" key from the provided properties map and returns the corresponding
  * list of extensions.
diff --git a/tests/python_tests/data/models.py b/tests/python_tests/data/models.py
index 494069aad6..aa0dd28c97 100644
--- a/tests/python_tests/data/models.py
+++ b/tests/python_tests/data/models.py
@@ -27,7 +27,17 @@ def get_models_list() -> tuple[str, ...]:
     )
 elif is_transformers_version(">=", "4.57"):
     # Restore after fix https://github.com/huggingface/optimum-intel/pull/1589
-    LINEAR_ATTENTION_MODELS_LIST = ("optimum-intel-internal-testing/tiny-random-qwen3-next",)
+    LINEAR_ATTENTION_MODELS_LIST = (
+        "optimum-intel-internal-testing/tiny-random-qwen3-next",
+        # Falcon-H1 (hybrid Mamba + attention) is enabled for GenAI: an explicit PagedAttention request now falls
+        # back to the stateful backend when the SDPAToPagedAttention transformation cannot rewrite the recurrent
+        # conv/ssm state (which otherwise fails with a dangling beam_idx parameter). Enable this entry once a
+        # non-degenerate tiny-random FalconH1 fixture is published under the optimum-intel-internal-testing
+        # namespace. The currently available public tiny-random FalconH1 checkpoints (e.g. tiny-random/falcon-h1,
+        # yujiepan/falcon-h1-tiny-random) use degenerate proportions (hidden_size=8, mamba_expand=32) that crash
+        # the Mamba naive kernel during generation and cannot serve as a reliable regression fixture.
+        # "optimum-intel-internal-testing/tiny-random-falcon-h1",
+    )
 
 
 GGUF_MODEL_LIST = (