const SHFMT_DRV_A = 0;
const SHFMT_DRV_B = 1;
const SHFMT_ID_DEFAULT = $FFFF;
const SHFMT_OPT_QUICKFORMAT = 0;
const SHFMT_OPT_FULLFORMAT = 1;
const SHFMT_OPT_SYSONLY = 2;
const SHFMT_ERROR = -1;
const SHFMT_CANCEL = -2;
const SHFMT_NOFORMAT = -3;
function SHFormatDrive(hWnd : HWND;
  Drive : Word;
  fmtID : Word;
  Options : Word) : Longint
  stdcall; external 'Shell32.dll' name 'SHFormatDrive';

...
implementation
...

procedure TForm1.Button1Click(Sender: TObject);
var
  FmtRes: longint;
begin
  try
    FmtRes:= ShFormatDrive(Handle,
      SHFMT_DRV_A,
      SHFMT_ID_DEFAULT,
      SHFMT_OPT_QUICKFORMAT);
    case FmtRes of
      SHFMT_ERROR :
        ShowMessage('Error formatting the drive');
      SHFMT_CANCEL :
        ShowMessage('User canceled formatting the drive');
      SHFMT_NOFORMAT :
        ShowMessage('No Format')
    else
      ShowMessage('Disk has been formatted');
    end;
  except
  end;
end;