The match took place at Hampden Park on 20 April 1957 and was contested by Division One clubs Falkirk and Kilmarnock.
Kilmarnock needed a replay to knock out the club who defeated them in their last final appearance also, East Fife.
Kilmarnock were making their sixth appearance in their history, winning twice, the last victory coming in 1929.
Falkirk took the lead after 33 minutes when John Prentice scored from the penalty spot after a foul by Willie Toner.
With no goals in the second half, the scores remained level to force a replay four days later.