diff --git a/lib/safetensors.ex b/lib/safetensors.ex
index 4258196..88d3730 100644
--- a/lib/safetensors.ex
+++ b/lib/safetensors.ex
@@ -41,6 +41,70 @@ defmodule Safetensors do
 
   @dtype_to_type for {k, v} <- @type_to_dtype, into: %{}, do: {v, k}
 
+  @doc """
+  Writes a map of tensors to a file.
+
+  Tensors are written into the file one by one, without the need to
+  dump all of them into the memory at once.
+  """
+  @spec write!(path :: Path.t(), %{String.t() => Nx.Tensor.t()}) :: :ok
+  def write!(path, tensors) when is_map(tensors) do
+    File.open!(path, [:write, :raw], fn file ->
+      tensors = Enum.sort(tensors)
+
+      {header_entries, _offset} =
+        Enum.map_reduce(tensors, 0, fn {tensor_name, tensor}, offset ->
+          tensor_header_entry(tensor_name, tensor, offset)
+        end)
+
+      :ok = :file.write(file, header_binary(header_entries))
+
+      for {_tensor_name, tensor} <- tensors do
+        :ok = :file.write(file, tensor_to_binary(tensor))
+      end
+    end)
+
+    :ok
+  end
+
+  defp tensor_header_entry(tensor_name, tensor, offset) do
+    end_offset = offset + tensor_byte_size(tensor)
+
+    header_entry = {
+      tensor_name,
+      Jason.OrderedObject.new(
+        dtype: tensor |> Nx.type() |> type_to_dtype(),
+        shape: tensor |> Nx.shape() |> Tuple.to_list(),
+        data_offsets: [offset, end_offset]
+      )
+    }
+
+    {header_entry, end_offset}
+  end
+
+  defp header_binary(header_entries) do
+    header_json =
+      header_entries
+      |> Jason.OrderedObject.new()
+      |> Jason.encode!()
+
+    [<<byte_size(header_json)::unsigned-64-integer-little>>, header_json]
+  end
+
+  defp tensor_byte_size(tensor) do
+    {_, elem_size} = Nx.type(tensor)
+    elem_byte_size = div(elem_size, 8)
+    Nx.size(tensor) * elem_byte_size
+  end
+
+  defp tensor_to_binary(tensor) do
+    {_, elem_size} = Nx.type(tensor)
+
+    tensor
+    |> Nx.to_binary()
+    |> new_byte_order(elem_size, :little)
+  end
+
   @doc """
   Serializes the given map of tensors to iodata.
 
@@ -50,46 +114,23 @@ defmodule Safetensors do
   """
   @spec dump(%{String.t() => Nx.Tensor.t()}) :: iodata()
   def dump(tensors) when is_map(tensors) do
+    tensors = Enum.sort(tensors)
+
     {header_entries, {buffer, _offset}} =
       Enum.map_reduce(tensors, {[], 0}, fn {tensor_name, tensor}, {buffer, offset} ->
-        {_, elem_size} = Nx.type(tensor)
-
-        binary =
-          tensor
-          |> Nx.to_binary()
-          |> new_byte_order(elem_size, :little)
-
-        end_offset = offset + byte_size(binary)
-
-        header_entry = {
-          tensor_name,
-          Jason.OrderedObject.new(
-            dtype: tensor |> Nx.type() |> type_to_dtype(),
-            shape: tensor |> Nx.shape() |> Tuple.to_list(),
-            data_offsets: [offset, end_offset]
-          )
-        }
-
+        {header_entry, end_offset} = tensor_header_entry(tensor_name, tensor, offset)
+        binary = tensor_to_binary(tensor)
         {header_entry, {[buffer, binary], end_offset}}
       end)
 
-    header_json =
-      header_entries
-      |> Jason.OrderedObject.new()
-      |> Jason.encode!()
-
-    [
-      <<byte_size(header_json)::unsigned-64-integer-little>>,
-      header_json,
-      buffer
-    ]
+    [header_binary(header_entries), buffer]
   end
 
   @doc """
-  Reads a safe tensor from file.
+  Reads a serialized map of tensors from a file.
 
-  Tensors are loaded into Nx one by one,
-  without the need to load the entire file from disk into memory.
+  Tensors are loaded into Nx one by one, without the need to load the
+  entire file from disk into memory.
   """
   @spec read!(path :: Path.t()) :: %{String.t() => Nx.Tensor.t()}
   def read!(path) do
diff --git a/test/safetensors_test.exs b/test/safetensors_test.exs
index ea444e4..a20430b 100644
--- a/test/safetensors_test.exs
+++ b/test/safetensors_test.exs
@@ -3,6 +3,20 @@ defmodule SafetensorsTest do
 
   doctest Safetensors
 
+  @tag :tmp_dir
+  test "write", %{tmp_dir: tmp_dir} do
+    path = Path.join(tmp_dir, "safetensor")
+
+    data = %{test: Nx.tensor([[1, 2], [3, 4]], type: :s32)}
+    Safetensors.write!(path, data)
+
+    # source:
+    # https://github.com/huggingface/safetensors/blob/1a65a3fdebcf280ef0ca32934901d3e2ad3b2c65/bindings/python/tests/test_simple.py#L22-L25
+    # with the header padding removed and changed numbers
+    assert File.read!(path) ==
+             ~s(<\x00\x00\x00\x00\x00\x00\x00{"test":{"dtype":"I32","shape":[2,2],"data_offsets":[0,16]}}\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00\x04\x00\x00\x00)
+  end
+
   test "dump" do
     binary =
       %{test: Nx.tensor([[1, 2], [3, 4]], type: :s32)}