The 1939–40 Greek Football Cup was the fourth edition of the Greek Football Cup. The competition culminated with the Greek Cup Final, held at Leoforos Alexandras Stadium, on 2 June 1940. The match was contested by Panathinaikos and Aris, with Panathinaikos winning by 3–1.^[1]

In the knockout phase, teams play against each other over a single match. If the match ends up as a draw, extra time will be played and if the match remains a draw a replay match is set at the home of the guest team which the extra time rule stands as well. That procedure will be repeated until a winner occurs.
The mechanism of the draws for each round is as follows:

• In the draw for the round of 16, the eight top teams of each association are seeded and the eight clubs that passed the qualification round are unseeded.
  The seeded teams are drawn against the unseeded teams.
• In the draws for the quarter-finals onwards, there are no seedings, and teams from the same group can be drawn against each other.

The 4th Greek Cup Final was played at the Leoforos Alexandras Stadium.

Chantzos Syrkos Tasos Kritikos Strouboulis Kaberos Svolopoulos Antonis Migiakis Dimitris Baltasis Symeonidis Takis Triantafyllis Olysseas Tsoutsos Manager: Dimitris Dimitriadis

Kostas Gotsis Achileas Magras Vahakn Abrahamyan Dimitris Stavrakbeis Alekos Siotis Kostas Nikolaidis Dimosthenis Chatzinikolaou Sidiropoulos Kleanthis Vikelidis Nikos Rammos Michalis Koloniaris Manager: Kostas Vikelidis