The 1959–60 Cupa României was the 22nd edition of Romania's most prestigious football cup competition.
It is the third season in the history of Cupa României when all the games are played on a neutral location.
If a match is drawn after 90 minutes, the game goes in extra time, and if the scored is still tight after 120 minutes, then a replay will be played.
In case the game is still tight after the replay, then the team from lower division will qualify for the next round.
From the first edition, the teams from Divizia A entered in competition in sixteen finals, rule which remained till today.