1985–86 Albanian Cup (Albanian: Kupa e Shqipërisë) was the thirty-fourth season of Albania's annual cup competition. It began on August 1985 with the First Round and ended on May 1986 with the Final match. The winners of the competition qualified for the 1986-87 first round of the UEFA Cup. KS Flamurtari were the defending champions, having won their first Albanian Cup last season. The cup was won by KF Tirana.
The rounds were played in a two-legged format similar to those of European competitions. If the aggregated score was tied after both games, the team with the higher number of away goals advanced. If the number of away goals was equal in both games, the match was decided by extra time and a penalty shootout, if necessary.