“The Parent Trap” is based on story elements so ancient and foolproof, they must have their roots in Shakespeare’s day: the twins changing places, their divorced parents falling in love again, and, for low comedy, their servants falling in love, too. And of course there’s a wicked would-be stepmother lurking about. It’s the stuff of Elizabethan comedy, resurrected in modern times as the British film “Twice Upon a Time” in 1953, and in the classic 1961 film “The Parent Trap.” The story is ageless and so is the gimmick: The twins are played by the same actress, using trick photography. Hayley Mills did it in 1961, and Lindsay Lohan does it this time, seamlessly.

“I’ll teach you to be me, and you teach me to be you,” one twin says, after they meet by chance at summer camp and realize that they’ve been raised separately by divorced parents. It’s a splendid story premise, but in a way, the switch is just the setup, and the real story involves the parents. They’re played by Dennis Quaid and Natasha Richardson, who bring humor and warmth to the movie.

The three important supporting roles are also well-filled. Plump, spunky Lisa Ann Walter plays the nanny and housekeeper on Quaid’s spread (he runs a vineyard in the Napa Valley), and bald, droll Simon Kunz is Richardson’s butler (she’s a trendy London fashion designer). Elaine Hendrix is the snotty publicist who plans to marry Quaid — until the parent trap springs. She has a thankless role — the only person in the movie we’re not supposed to like. She gets to earn her stripes in a camping trip during which she demonstrates, once and for all, that she is not the ideal wife for Quaid.

Quaid is instantly likable, with that goofy smile. Richardson, who almost always plays tougher roles and harder women, this time is warm and attractive.

Movies like this remember how much fun escapism can be. The film opens with Quaid and Richardson falling in love on the Queen Elizabeth 2 ocean liner and being married mid-Atlantic. The film includes the kind of summer camp where when the kids play pranks, it looks like they had the help of a platoon of art directors and special-effects coordinators. And of course both parents live in great houses: Richardson in a London town house with sweeping staircases and Architectural Digest interiors, Quaid in a Napa ranch home with a shaded veranda. The key task is to make the double photography of the “twins” work. All kinds of tricks are used, and of course the techniques are more advanced than they were in 1961. Lindsay Lohan has command of flawless British and American accents, and also uses slightly flawed ones for when the girls are playing each other. This is a family picture that’s not too soppy for adults. (SD-Agencies)