diff --git a/core/src/main/java/hudson/FilePath.java b/core/src/main/java/hudson/FilePath.java
index a81ea7772a..943d7eb7d8 100644
--- a/core/src/main/java/hudson/FilePath.java
+++ b/core/src/main/java/hudson/FilePath.java
@@ -1664,11 +1664,11 @@ public final class FilePath implements Serializable {
         return act(new FileCallable<String>() {
             private static final long serialVersionUID = 1L;
             public String invoke(File f, VirtualChannel channel) throws IOException {
-                BufferedInputStream source = new BufferedInputStream(new FileInputStream(f));
+                FileInputStream is = new FileInputStream(f);
                 try {
-                    return Util.getDigestOf(source);
+                    return Util.getDigestOf(new BufferedInputStream(is));
                 } finally {
-                    source.close();
+                    is.close();
                 }
             }
         });
diff --git a/core/src/main/java/hudson/Util.java b/core/src/main/java/hudson/Util.java
index 47ad0bc665..818a26d767 100644
--- a/core/src/main/java/hudson/Util.java
+++ b/core/src/main/java/hudson/Util.java
@@ -554,7 +554,11 @@ public class Util {
      * @see DigestUtils#md5(InputStream)
      */
     public static String getDigestOf(InputStream source) throws IOException {
-        return DigestUtils.md5Hex(source);
+        try {
+            return DigestUtils.md5Hex(source);
+        } finally {
+            source.close();
+        }
     }
 
     public static String getDigestOf(String text) {