[AND_REY]

Как то так:

Код:

procedure TForm1.Button1Click(Sender: TObject);
Var
 F: File of Char;
 Glas: Set of Char;
 N: Integer;
 C: Char;
begin
 N:= 0;
 Glas:= ['а','и','о','у','ы','э','А','И','О','У','Ы','Э'];
 AssignFile(F, 'C:\1.txt');
 Reset(F);
 While Not (Eof(F)) do
  begin
   Read(F, C);
   if (C In Glas) Then Inc(N);
  end;
 ShowMessage('Гласных: '+IntToStr(N));
 CloseFile(F);
end;