diff --git a/src/anthropic/_base_client.py b/src/anthropic/_base_client.py
index 963cd1b9..bc34419a 100644
--- a/src/anthropic/_base_client.py
+++ b/src/anthropic/_base_client.py
@@ -368,7 +368,7 @@ class BaseClient(Generic[_HttpxClientT, _DefaultStreamT]):
     _client: _HttpxClientT
     _version: str
     _base_url: URL
-    max_retries: int
+    max_retries: int | float
     timeout: Union[float, Timeout, None]
     _strict_response_validation: bool
     _idempotency_header: str | None
@@ -380,7 +380,7 @@ def __init__(
         version: str,
         base_url: str | URL,
         _strict_response_validation: bool,
-        max_retries: int = DEFAULT_MAX_RETRIES,
+        max_retries: int | float = DEFAULT_MAX_RETRIES,
         timeout: float | Timeout | None = DEFAULT_TIMEOUT,
         custom_headers: Mapping[str, str] | None = None,
         custom_query: Mapping[str, object] | None = None,
@@ -913,7 +913,7 @@ def __init__(
         *,
         version: str,
         base_url: str | URL,
-        max_retries: int = DEFAULT_MAX_RETRIES,
+        max_retries: int | float = DEFAULT_MAX_RETRIES,
         timeout: float | Timeout | None | NotGiven = not_given,
         http_client: httpx.Client | None = None,
         custom_headers: Mapping[str, str] | None = None,
@@ -1047,7 +1047,15 @@ def request(
         max_retries = input_options.get_max_retries(self.max_retries)
 
         retries_taken = 0
-        for retries_taken in range(max_retries + 1):
+        # Cap max_retries for range() — math.inf is a float and cannot be passed
+        # to range(). The error message in __init__ advertises math.inf as valid,
+        # so we must handle it here. Use sys.maxsize as the effective upper bound.
+        # Also wrap with int() to handle finite floats like 2.0 (range(3.0) raises TypeError).
+        if max_retries == math.inf or max_retries >= sys.maxsize:
+            range_limit = sys.maxsize
+        else:
+            range_limit = int(max_retries) + 1
+        for retries_taken in range(range_limit):
             options = model_copy(input_options)
             options = self._prepare_options(options)
 
@@ -1552,7 +1560,7 @@ def __init__(
         version: str,
         base_url: str | URL,
         _strict_response_validation: bool,
-        max_retries: int = DEFAULT_MAX_RETRIES,
+        max_retries: int | float = DEFAULT_MAX_RETRIES,
         timeout: float | Timeout | None | NotGiven = not_given,
         http_client: httpx.AsyncClient | None = None,
         custom_headers: Mapping[str, str] | None = None,
@@ -1687,7 +1695,13 @@ async def request(
         max_retries = input_options.get_max_retries(self.max_retries)
 
         retries_taken = 0
-        for retries_taken in range(max_retries + 1):
+        # Cap max_retries for range() — math.inf is a float and cannot be passed
+        # to range(). Also wrap with int() to handle finite floats like 2.0 (range(3.0) raises TypeError).
+        if max_retries == math.inf or max_retries >= sys.maxsize:
+            range_limit = sys.maxsize
+        else:
+            range_limit = int(max_retries) + 1
+        for retries_taken in range(range_limit):
             options = model_copy(input_options)
             options = await self._prepare_options(options)
 
diff --git a/src/anthropic/_models.py b/src/anthropic/_models.py
index 2d979355..be7cd3a3 100644
--- a/src/anthropic/_models.py
+++ b/src/anthropic/_models.py
@@ -878,7 +878,7 @@ class Config(pydantic.BaseConfig):  # pyright: ignore[reportDeprecated]
     else:
         model_config: ClassVar[ConfigDict] = ConfigDict(arbitrary_types_allowed=True)
 
-    def get_max_retries(self, max_retries: int) -> int:
+    def get_max_retries(self, max_retries: int | float) -> int | float:
         if isinstance(self.max_retries, NotGiven):
             return max_retries
         return self.max_retries