An airline ticket can get you to Las Vegas quite reasonably these days. A time machine that’ll get you there a half-century ago is another matter.

That’s the goal of The Rat Pack – Live at the Sands, the London hit that Dallas Summer Musicals brought to the Majestic Theatre on Tuesday.

You can guess the format from the title: Singers portraying Frank Sinatra, Dean Martin and Sammy Davis Jr. cover the stars’ greatest hits. A 16-piece band (something of a luxury in the theater these days) plays onstage, and three curvaceous backup singers add a considerable amount of what in those days was called sex appeal.

This may sound like a dubious proposition, but people apparently are still eager to hear numbers out of the great American songbook (alongside tunes of lesser pedigree) sung by voices of substance and backed by choirs of actual saxes, trumpets and trombones.

Of the three leading performers, only Stephen Triffitt’s Sinatra provokes the occasional internal double take, providing reassurance that this is only a latter-day impersonator rather than the real thing. At first, he’s almost too successful in duplicating Sinatra’s every rhythmic and phonetic inflection. Eventually, he makes us forget the mechanics and just listen to the music – especially the torch song “Angel Eyes.” He’s also got the physical manner, at once regal and offhand, down pat.

His pretend buddies both boast fine voices, but the illusion is weaker. Davis sometimes trod perilously close to self-parody, which makes things doubly hard for David Hayes. He’s lively and he can hoof it, but he lacks the grit under the original star’s larger-than-life exterior. Mark Adams projects Martin’s macho appeal, and the voice evokes the star without imitating him slavishly. But Adams works too hard at ingratiating himself with the audience, whereas you could always see a dead chill of indifference in Martin’s eyes.

The Rat Pack brims with the buddies’ horseplay (complete with sexist, racist and boozy jokes authentic to the period). What it leaves you with, however, are meditations on Frank Sinatra’s unique career. Not only does Triffitt bring him to life, he sings the questionable later material, especially “My Way,” with genuine feeling that we didn’t always get from the man himself.

PLAN YOUR LIFE

Through Sunday at the Majestic Theatre. Runs 140 mins. $12 to $71. Ticketmaster at 214-631-2787, www.ticketmaster.com.