| Albanian Cup | |
| Year: | 1960 |
| Other Titles: | Kupa e Shqipërisë |
| Country: | Albania |
| Winners: | Dinamo Tirana |
| Second: | Flamurtari |
| Prev Season: | 1958 |
| Next Season: | 1961 |
1960 Albanian Cup (Albanian: Kupa e Shqipërisë) was the eleventh season of Albania's annual cup competition. It began in Spring 1960 with the First Round and ended in May 1960 with the Final matches. Partizani were the defending champions, having won their fourth Albanian Cup last season.
The cup was won by Dinamo Tirana.[1]
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.
Games were played in March, 1960*
All sixteen teams of the 1958 Superliga and First Division entered in this round. First and second legs were played in March, 1960.
|}
In this round entered the 8 winners from the previous round.
|}+ Flamurtari won by corners.
In this round entered the four winners from the previous round.
|}
In this round entered the two winners from the previous round.
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