They said it could not be done, and the official history of the island prison says it never was done: no one ever escaped from Alcatraz Island during the 29 years (1934-63) it was a federal penitentiary.
Frank Lee Morris, Clarence and John Anglin were never recaptured and opinion is divided as to whether they succeeded in their escape, were drowned or eaten by sharks.
The FBI spent years investigating the case and finally concluded the men had failed.
The film "Escape from Alactraz" (1979) was based on this attempt, starring Clint Eastwood as Frank Morris.
The MythBusters looked into it: [watch video]
Did three prisoners in 1962 build a raft out of raincoats and use it to escape from Alcatraz?
Even though they have their doubts that Morris and the Anglin brothers made it, they deemed it "Plausible".
According to Alcatraz History:
... to this day there are five prisoners listed as "missing and presumed drowned."
How legitimate is it to "pressume" that one of those missing prisoners didn't drown?
Are there clues that suggest an escapee survived?