diff --git a/tests/engine/test_computed_prefix_blocks.py b/tests/engine/test_computed_prefix_blocks.py
new file mode 100644
index 000000000000..ed35212cc3f1
--- /dev/null
+++ b/tests/engine/test_computed_prefix_blocks.py
@@ -0,0 +1,34 @@
+import pytest
+
+from vllm.engine.arg_utils import EngineArgs
+from vllm.engine.llm_engine import LLMEngine
+from vllm.sampling_params import SamplingParams
+
+
+@pytest.mark.parametrize("model", ["facebook/opt-125m"])
+@pytest.mark.parametrize("block_size", [16])
+def test_computed_prefix_blocks(model: str, block_size: int):
+    # This test checks if we are able to run the engine to completion
+    # without triggering asserts.
+    # We are in a scenario where all blocks from the second request's prompt
+    # are full and already computed when the second request arrives.
+    prompt = (
+        "You are a helpful assistant. How do I build a car from cardboard and "
+        "paper clips? Is there an easy to follow video tutorial available "
+        "online for free?")
+    prompt2 = (
+        " Please recommend to me some resources where I can learn not only to "
+        "handle technical difficulties of building a car, but also "
+        "decoration.")
+
+    engine_args = EngineArgs(model=model,
+                             block_size=block_size,
+                             enable_prefix_caching=True)
+
+    engine = LLMEngine.from_engine_args(engine_args)
+    sampling_params = SamplingParams()
+
+    engine.add_request("0", prompt + prompt2, sampling_params)
+    engine.step()
+    engine.add_request("1", prompt, sampling_params)
+    engine.step()
diff --git a/vllm/core/block_manager.py b/vllm/core/block_manager.py
index daf83827a7e5..52b120f227ed 100644
--- a/vllm/core/block_manager.py
+++ b/vllm/core/block_manager.py
@@ -1,6 +1,6 @@
 """A block manager that manages token blocks."""
 import enum
-from itertools import count
+from itertools import count, takewhile
 from os.path import commonprefix
 from typing import Dict, List, Optional, Set, Tuple
 
@@ -426,23 +426,29 @@ class BlockSpaceManager:
         for block in block_table:
             block.last_accessed = access_time
 
-    def compute_last_full_block_in_seq(self, seq: Sequence):
+    def compute_full_blocks_in_seq(self, seq: Sequence):
         if seq.seq_id not in self.block_tables:
             return
         max_full_block = seq.get_len() // self.block_size - 1
         block_table = self.block_tables[seq.seq_id]
         if max_full_block == -1:
             return
-        block_table[max_full_block].computed = True
+        for i in reversed(range(max_full_block)):
+            if block_table[i].computed:
+                break
+            block_table[i].computed = True
 
-    def get_all_block_ids_till_computed(self, seq: Sequence) -> List[int]:
+    def get_all_computed_blocks(self, seq: Sequence) -> List[int]:
         if seq.seq_id not in self.block_tables:
             return []
         block_table = self.block_tables[seq.seq_id]
-        for block_idx in reversed(range(len(block_table))):
-            if block_table[block_idx].computed:
-                return [b.block_number for b in block_table[:block_idx + 1]]
-        return []
+        # NOTE We exclude the last block to avoid the case where the entire
+        # prompt is cached. This would cause erroneous behavior in model
+        # runner.
+        return [
+            b.block_number
+            for b in takewhile(lambda b: b.computed, block_table[:-1])
+        ]
 
     def get_common_computed_block_ids(self,
                                       seq_group: SequenceGroup) -> List[int]:
@@ -451,14 +457,12 @@ class BlockSpaceManager:
             return []
 
         ids_list = [
-            self.get_all_block_ids_till_computed(seq)
+            self.get_all_computed_blocks(seq)
             for seq in iter(seq_group.seqs_dict.values())
         ]
         return commonprefix([ids for ids in ids_list if ids != []])
 
     def mark_blocks_as_computed(self, seq_group: SequenceGroup):
-        # NOTE: We only mark the last full block because with prefix caching,
-        # all blocks until the marked one are guaranteed to be computed.
         if self.enable_caching:
             for seq in seq_group.seqs_dict.values():
-                self.compute_last_full_block_in_seq(seq)
+                self.compute_full_blocks_in_seq(seq)
diff --git a/vllm/worker/model_runner.py b/vllm/worker/model_runner.py
index b01f865f1bb0..9023b0c59b3f 100644
--- a/vllm/worker/model_runner.py
+++ b/vllm/worker/model_runner.py
@@ -215,6 +215,7 @@ class ModelRunner:
                 slot_mapping[-1].append(slot)
 
         max_prompt_len = max(subquery_lens)
+        assert max_prompt_len > 0
         input_tokens = _make_tensor_with_pad(input_tokens,
                                              max_prompt_len,
                                              pad=0,