Procedure CopyFileWithProgressBar(SourceFile, TargetFile: string);
  var FromFile, ToFile: file of byte;
        Buffer: array[0..4096] of Char;
        NumRead: integer;
        FileLength: longint;
begin
 AssignFile(FromFile, SourceFile);
 Reset(FromFile);
 AssignFile(ToFile, TargetFile);
 Rewrite(ToFile);
 FileLength:=FileSize(FromFile);
  with Form1.Progressbar1 do
   begin
    Min:=0;
    Max:=FileLength;
     while FileLength > 0 do
      begin
       BlockRead(FromFile, Buffer[0], SizeOf(Buffer), NumRead);
       FileLength:=FileLength - NumRead;
       BlockWrite(ToFile, Buffer[0], NumRead);
       Position:=Position + NumRead;
       Application.ProcessMessages;
      end;
    CloseFile(FromFile);
    CloseFile(ToFile);
   end;
end;

Zdroj: http://havelka.wz.cz