diff --git a/core/src/main/java/org/testcontainers/containers/ContainerState.java b/core/src/main/java/org/testcontainers/containers/ContainerState.java
index b3a38febf73..b289f35f7a3 100644
--- a/core/src/main/java/org/testcontainers/containers/ContainerState.java
+++ b/core/src/main/java/org/testcontainers/containers/ContainerState.java
@@ -22,14 +22,17 @@
 import org.testcontainers.utility.MountableFile;
 import org.testcontainers.utility.ThrowingFunction;
 
-import java.io.ByteArrayInputStream;
-import java.io.ByteArrayOutputStream;
+import java.io.BufferedInputStream;
+import java.io.BufferedOutputStream;
 import java.io.File;
 import java.io.FileOutputStream;
 import java.io.IOException;
 import java.io.InputStream;
+import java.io.OutputStream;
 import java.nio.charset.Charset;
 import java.nio.charset.StandardCharsets;
+import java.nio.file.Files;
+import java.nio.file.Path;
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Map;
@@ -345,21 +348,32 @@ default void copyFileToContainer(Transferable transferable, String containerPath
             throw new IllegalStateException("copyFileToContainer can only be used with created / running container");
         }
 
+        Path tempFile = Files.createTempFile("tc-", "-copy");
+
         try (
-            ByteArrayOutputStream byteArrayOutputStream = new ByteArrayOutputStream();
-            TarArchiveOutputStream tarArchive = new TarArchiveOutputStream(byteArrayOutputStream)
+            OutputStream os = Files.newOutputStream(tempFile);
+            BufferedOutputStream bos = new BufferedOutputStream(os);
+            TarArchiveOutputStream tarArchive = new TarArchiveOutputStream(bos)
         ) {
             tarArchive.setLongFileMode(TarArchiveOutputStream.LONGFILE_POSIX);
             tarArchive.setBigNumberMode(TarArchiveOutputStream.BIGNUMBER_POSIX);
 
             transferable.transferTo(tarArchive, containerPath);
             tarArchive.finish();
-
-            getDockerClient()
-                .copyArchiveToContainerCmd(getContainerId())
-                .withTarInputStream(new ByteArrayInputStream(byteArrayOutputStream.toByteArray()))
-                .withRemotePath("/")
-                .exec();
+            bos.flush();
+
+            try (
+                InputStream is = Files.newInputStream(tempFile);
+                BufferedInputStream bis = new BufferedInputStream(is)
+            ) {
+                getDockerClient()
+                    .copyArchiveToContainerCmd(getContainerId())
+                    .withTarInputStream(bis)
+                    .withRemotePath("/")
+                    .exec();
+            }
+        } finally {
+            Files.deleteIfExists(tempFile);
         }
     }
 
diff --git a/core/src/test/java/org/testcontainers/junit/FileOperationsTest.java b/core/src/test/java/org/testcontainers/junit/FileOperationsTest.java
index d9655443480..4b3aa804b50 100644
--- a/core/src/test/java/org/testcontainers/junit/FileOperationsTest.java
+++ b/core/src/test/java/org/testcontainers/junit/FileOperationsTest.java
@@ -3,15 +3,19 @@
 import com.github.dockerjava.api.exception.NotFoundException;
 import org.apache.commons.io.FileUtils;
 import org.apache.commons.io.IOUtils;
+import org.apache.commons.io.output.CountingOutputStream;
 import org.junit.Rule;
 import org.junit.Test;
 import org.junit.rules.TemporaryFolder;
 import org.testcontainers.TestImages;
+import org.testcontainers.containers.Container;
 import org.testcontainers.containers.GenericContainer;
 import org.testcontainers.containers.startupcheck.OneShotStartupCheckStrategy;
 import org.testcontainers.utility.MountableFile;
 
+import java.io.BufferedOutputStream;
 import java.io.File;
+import java.io.FileOutputStream;
 import java.io.IOException;
 
 import static org.assertj.core.api.Assertions.assertThat;
@@ -40,6 +44,43 @@ public void copyFileToContainerFileTest() throws Exception {
         }
     }
 
+    @Test
+    public void copyLargeFilesToContainer() throws Exception {
+        File tempFile = temporaryFolder.newFile();
+        try (
+            GenericContainer alpineCopyToContainer = new GenericContainer(TestImages.ALPINE_IMAGE) //
+                .withCommand("sleep", "infinity")
+        ) {
+            alpineCopyToContainer.start();
+            final long byteCount;
+            try (
+                FileOutputStream fos = new FileOutputStream(tempFile);
+                CountingOutputStream cos = new CountingOutputStream(fos);
+                BufferedOutputStream bos = new BufferedOutputStream(cos)
+            ) {
+                for (int i = 0; i < 0x4000; i++) {
+                    byte[] bytes = new byte[0xFFFF];
+                    bos.write(bytes);
+                }
+                bos.flush();
+                byteCount = cos.getByteCount();
+            }
+            final MountableFile mountableFile = MountableFile.forHostPath(tempFile.getPath());
+            final String containerPath = "/test.bin";
+            alpineCopyToContainer.copyFileToContainer(mountableFile, containerPath);
+
+            final Container.ExecResult execResult = alpineCopyToContainer.execInContainer( //
+                "stat",
+                "-c",
+                "%s",
+                containerPath
+            );
+            assertThat(execResult.getStdout()).isEqualToIgnoringNewLines(Long.toString(byteCount));
+        } finally {
+            tempFile.delete();
+        }
+    }
+
     @Test
     public void copyFileToContainerFolderTest() throws Exception {
         try (