uses ShellApi;

Function CopyDirContent(SourceDir, Mask, TargetDir: string): boolean;
  var FileOp: TSHFileOpStruct;
begin
 ZeroMemory(@FileOp, SizeOf(FileOp));
  if SourceDir[Length(SourceDir)] <> '\' then SourceDir:=SourceDir + '\';
  with FileOp do
   begin
    Wnd:=Form1.Handle;
    wFunc:=FO_COPY;
    pFrom:=PChar(SourceDir + Mask);
    pTo:=PChar(TargetDir);
    fFlags:=FOF_ALLOWUNDO or FOF_SILENT or FOF_NOCONFIRMATION or FOF_NOCONFIRMMKDIR;
   end;
  if (SHFileOperation(FileOp) <> 0) or (FileOp.fAnyOperationsAborted) then Result:=False
   else Result:=True;
end;

Zdroj: http://havelka.wz.cz