1995–96 Albanian Cup (Albanian: Kupa e Shqipërisë) was the forty-fourth season of Albania's annual cup competition. It began in August 1995 with the First Round and ended in May 1996 with the Final match. The winners of the competition qualified for the 1996-97 first round of the UEFA Cup. Teuta were the defending champions, having won their first Albanian Cup last season. The cup was won by Tirana.