The madcap plot centers on Paris-based playboy Bernard (Allam), who has three air hostess fiancées, played by Daisy Beaumont, Michelle Gomez and Tamzin Outhwaite.
When his school friend Robert (Rylance) arrives, Bernard relishes the chance to show his friend his first-class operation at work. But Bernard hadn't reckoned on a change of airline schedules. Frances de la Tour plays his long-suffering housekeeper.
Boeing-Boeing originally opened in London in the mid-sixties, held the world record for the longest-running comedy in the West End, playing over 2,000 performances before transferring to Broadway.
In 1965 John Rich directed the film starring Tony Curtis and Jerry Lewis. Allam was last seen on the West End stage in David Harrower's Blackbird. His Best Actor Olivier came with the Donmar production of Privates on Parade.
The multi award-winning Frances de la Tour was most recently seen onstage with the original cast of Bennett's The History Boys. For the Broadway version she received a Tony for Best Featured Actress.
Rylance was the previous artistic director of the Shakespeare Globe. In the West End he won an Olivier for playing Benedick in Warchus' 1993 production of Much Ado About Nothing.
Beaumont, Outhwaite and Gomez are best known for their television roles.
Speaking to Variety, producer Sonia Friedman said of the revival, "Boeing-Boeing really is very funny, and I think we're at a point now where we can stage plays from an era that was politically incorrect, so long as we're knowing about it. And remember, the women in the play are not being exploited: They're enjoying themselves tremendously."
For more on Boeing-Boeing, which is booking until April 28, call (0)870 0606637.