diff --git a/replicate/exceptions.py b/replicate/exceptions.py
index 6302d10f..497f522d 100644
--- a/replicate/exceptions.py
+++ b/replicate/exceptions.py
@@ -10,6 +10,12 @@ class ReplicateException(Exception):
 class ModelError(ReplicateException):
     """An error from user's code in a model."""
 
+    prediction_id: str
+
+    def __init__(self, error: Optional[str], prediction_id: str) -> None:
+        self.prediction_id = prediction_id
+        super().__init__(error)
+
 
 class ReplicateError(ReplicateException):
     """
diff --git a/replicate/prediction.py b/replicate/prediction.py
index 871566d7..b5590682 100644
--- a/replicate/prediction.py
+++ b/replicate/prediction.py
@@ -249,7 +249,7 @@ def output_iterator(self) -> Iterator[Any]:
             self.reload()
 
         if self.status == "failed":
-            raise ModelError(self.error)
+            raise ModelError(self.error, self.id)
 
         output = self.output or []
         new_output = output[len(previous_output) :]
@@ -272,7 +272,7 @@ async def async_output_iterator(self) -> AsyncIterator[Any]:
             await self.async_reload()
 
         if self.status == "failed":
-            raise ModelError(self.error)
+            raise ModelError(self.error, self.id)
 
         output = self.output or []
         new_output = output[len(previous_output) :]
diff --git a/replicate/run.py b/replicate/run.py
index 975cc4dc..7fcbbf06 100644
--- a/replicate/run.py
+++ b/replicate/run.py
@@ -58,7 +58,7 @@ def run(
     prediction.wait()
 
     if prediction.status == "failed":
-        raise ModelError(prediction.error)
+        raise ModelError(prediction.error, prediction.id)
 
     return prediction.output
 
@@ -97,7 +97,7 @@ async def async_run(
     await prediction.async_wait()
 
     if prediction.status == "failed":
-        raise ModelError(prediction.error)
+        raise ModelError(prediction.error, prediction.id)
 
     return prediction.output