diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4d93f3b..a66dc43 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Revision history for testcontainer-hs
 
+## 0.5.2.0 -- Unreleased
+
+* Introduce `withCopyFileToContainer` to copy local files to the container (@LaurentRDC, https://github.com/testcontainers/testcontainers-hs/pull/62)
+
 ## 0.5.1.0 -- 2025-01-14
 
 * Introduce `withWorkingDirectory` to set the working directory inside a container (@alexbiehl, https://github.com/testcontainers/testcontainers-hs/pull/37)
diff --git a/src/TestContainers.hs b/src/TestContainers.hs
index 5de3d57..0523200 100644
--- a/src/TestContainers.hs
+++ b/src/TestContainers.hs
@@ -31,6 +31,7 @@ module TestContainers
     M.setMemory,
     M.setCpus,
     M.withWorkingDirectory,
+    M.withCopyFileToContainer,
     M.withNetwork,
     M.withNetworkAlias,
     M.setLink,
diff --git a/src/TestContainers/Docker.hs b/src/TestContainers/Docker.hs
index 32b9646..b20eb2b 100644
--- a/src/TestContainers/Docker.hs
+++ b/src/TestContainers/Docker.hs
@@ -89,6 +89,7 @@ module TestContainers.Docker
     setRm,
     setEnv,
     withWorkingDirectory,
+    withCopyFileToContainer,
     withNetwork,
     withNetworkAlias,
     setLink,
@@ -160,7 +161,7 @@ where
 
 import Control.Concurrent (threadDelay)
 import Control.Exception (IOException, throw)
-import Control.Monad (forM_, replicateM, unless)
+import Control.Monad (forM_, replicateM, unless, void)
 import Control.Monad.Catch
   ( Exception,
     MonadCatch,
@@ -290,7 +291,8 @@ data ContainerRequest = ContainerRequest
     labels :: [(Text, Text)],
     noReaper :: Bool,
     followLogs :: Maybe LogConsumer,
-    workDirectory :: Maybe Text
+    workDirectory :: Maybe Text,
+    copyFilesToContainer :: [(FilePath, FilePath)]
   }
 
 instance WithoutReaper ContainerRequest where
@@ -326,7 +328,8 @@ containerRequest image =
       labels = mempty,
       noReaper = False,
       followLogs = Nothing,
-      workDirectory = Nothing
+      workDirectory = Nothing,
+      copyFilesToContainer = mempty
     }
 
 -- | Set the name of a Docker container. This is equivalent to invoking @docker run@
@@ -417,6 +420,27 @@ withWorkingDirectory :: Text -> ContainerRequest -> ContainerRequest
 withWorkingDirectory workdir request =
   request {workDirectory = Just workdir}
 
+-- | Copies a file from the host to the container. Call this function
+-- multiple times to copy multiple files to the container.
+--
+-- This can be used, for example, to initialize a database:
+--
+-- >>> :{
+--     containerRequest (fromTag "postgres:16-alpine")
+--         & withCopyFileToContainer "my-init-script.sql" "/docker-entrypoint-initdb.d/"
+-- :}
+--
+-- @since 0.5.2.0
+withCopyFileToContainer ::
+  -- | File on the host
+  FilePath ->
+  -- | Directory in the container
+  FilePath ->
+  ContainerRequest ->
+  ContainerRequest
+withCopyFileToContainer fileFromHost containerDirectory request =
+  request {copyFilesToContainer = copyFilesToContainer request <> [(fileFromHost, containerDirectory)]}
+
 -- | Set the network the container will connect to. This is equivalent to passing
 -- @--network network_name@ to @docker run@.
 --
@@ -558,7 +582,8 @@ run request = do
           labels,
           noReaper,
           followLogs,
-          workDirectory
+          workDirectory,
+          copyFilesToContainer
         } = request
 
   config@Config {configTracer, configCreateReaper} <-
@@ -580,35 +605,43 @@ run request = do
         Just . (prefix <>) . ("-" <>) . pack
           <$> replicateM 6 (Random.randomRIO ('a', 'z'))
 
-  let dockerRun :: [Text]
-      dockerRun =
+  -- Instead of using `docker run`, we use the more manual `docker create` + `docker start`.
+  -- This allows to get the container ID early from `docker create`, and thus
+  -- optionally copy files using `docker cp`.
+  let dockerCreate :: [Text]
+      dockerCreate =
         concat $
-          [["run"]]
-            ++ [["--detach"]]
-            ++ [["--name", containerName] | Just containerName <- [name]]
-            ++ [["--label", label <> "=" <> value] | (label, value) <- additionalLabels ++ labels]
+          [["create"]]
+            ++ [["--cpus", value] | Just value <- [cpus]]
             ++ [["--env", variable <> "=" <> value] | (variable, value) <- env]
-            ++ [["--publish", pack (show port) <> "/" <> protocol] | Port {port, protocol} <- exposedPorts]
+            ++ [["--label", label <> "=" <> value] | (label, value) <- additionalLabels ++ labels]
+            ++ [["--link", container] | container <- links]
+            ++ [["--memory", value] | Just value <- [memory]]
+            ++ [["--name", containerName] | Just containerName <- [name]]
             ++ [["--network", networkName] | Just (Right networkName) <- [network]]
             ++ [["--network", networkId dockerNetwork] | Just (Left dockerNetwork) <- [network]]
             ++ [["--network-alias", alias] | Just alias <- [networkAlias]]
-            ++ [["--link", container] | container <- links]
-            ++ [["--volume", src <> ":" <> dest] | (src, dest) <- volumeMounts]
+            ++ [["--publish", pack (show port) <> "/" <> protocol] | Port {port, protocol} <- exposedPorts]
             ++ [["--rm"] | rmOnExit]
+            ++ [["--volume", src <> ":" <> dest] | (src, dest) <- volumeMounts]
             ++ [["--workdir", workdir] | Just workdir <- [workDirectory]]
-            ++ [["--memory", value] | Just value <- [memory]]
-            ++ [["--cpus", value] | Just value <- [cpus]]
             ++ [[tag]]
-            ++ [command | Just command <- [cmd]]
 
-  stdout <- docker configTracer dockerRun
+  (id :: ContainerId) <- strip . pack <$> docker configTracer dockerCreate
+
+  forM_ copyFilesToContainer $ \(hostFile, containerFile) ->
+    docker configTracer ["cp", pack hostFile, id <> ":" <> pack containerFile]
+
+  let dockerStart :: [Text]
+      dockerStart =
+        concat $
+          [["start"]]
+            ++ [[id]]
+            ++ [command | Just command <- [cmd]]
 
-  let id :: ContainerId
-      !id =
-        -- N.B. Force to not leak STDOUT String
-        strip (pack stdout)
+  void $ docker configTracer dockerStart
 
-      -- Careful, this is really meant to be lazy
+  let -- Careful, this is really meant to be lazy
       ~inspectOutput =
         unsafePerformIO $
           internalInspect configTracer id
diff --git a/test/TestContainers/TastySpec.hs b/test/TestContainers/TastySpec.hs
index 854822f..a2fba0b 100644
--- a/test/TestContainers/TastySpec.hs
+++ b/test/TestContainers/TastySpec.hs
@@ -27,6 +27,7 @@ import TestContainers.Tasty
     waitUntilMappedPortReachable,
     waitUntilTimeout,
     withContainers,
+    withCopyFileToContainer,
     withFollowLogs,
     withNetwork,
     (&),
@@ -78,6 +79,11 @@ containers1 = do
         & setWaitingFor
           (waitForHttp "16686/tcp" "/" [200])
 
+  _postgres <-
+    run $
+      containerRequest (fromTag "postgres:16-alpine")
+        & withCopyFileToContainer "test/data/init-script.sql" "/docker-entrypoint-initdb.d/"
+
   _helloWorld <-
     run $
       containerRequest (fromTag "hello-world:latest")
diff --git a/test/data/init-script.sql b/test/data/init-script.sql
new file mode 100644
index 0000000..6131def
--- /dev/null
+++ b/test/data/init-script.sql
@@ -0,0 +1,6 @@
+
+create table customers (
+     id bigint not null,
+     name varchar not null,
+     primary key (id)
+);
\ No newline at end of file
diff --git a/testcontainers.cabal b/testcontainers.cabal
index 3fe2ba8..4e1a4d4 100644
--- a/testcontainers.cabal
+++ b/testcontainers.cabal
@@ -18,6 +18,7 @@ build-type:         Simple
 extra-source-files:
   CHANGELOG.md
   README.md
+  test/data/init-script.sql
 
 tested-with:
   GHC ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.4 || ==9.4.2 || ==9.8.2