The men on stage are impersonating Frank Sinatra, Dean Martin, Peter Lawford and Sammy Davis Jnr, but Rat Pack Confidential is not a tribute act. It's hard, though, to say just what it is. The ancient comedian Joey Bishop starts his act but is interrupted by a man in the audience who sings phrases of Sinatra hits, then rises to reveal that he is Sinatra. Frank takes the stage, and proposes summoning up Deano, Pete and Sammy so that they can all "hit the groove". "Hit the groove?" says Bishop, alarmed. "I'm nearly 80 years old." Frank replies, "And I'm dead."

The idea of Sinatra's being such a cool cat that he could take death in his stride is amusing, as is much about the show, adapted by Paul Sirett from Shawn Levy's book of the same title. But its raison d'être is confusing, to say the least. As the songs alternate with scenes from the performer's lives, we see the ugliness and squalor behind the back-slapping camaraderie: Dean's alcoholism, Sammy's struggles against racism, Frank's closeness to the Mafia and, along with Peter, pimping for the President of the United States.

The songs that accompany or follow the sketches comment ironically on them: Frank sings the childishly cheery "High Hopes" while Sammy is bullied and beaten by rednecks; as Frank solicits funds for John F Kennedy from the Mob, Peter softly sings "Pennies from Heaven". This may sound simple-minded, but the counterpoint is surprisingly, bitterly effective. I was even, to my astonishment, absorbed and moved when Frank, the end near, faces the final curtain and delivers you know what. Instead of Sinatra's thuggish sententiousness, the singer gives it a bare honesty with a touch of defensiveness and of wonderment at the road he has travelled.

But is Giles Croft's production meant to inform us? To shock us? To evoke our anger? Our pity? The seamy anecdotes are no match for the potent music, which drowns any indignation we may feel in romantic yearning when Frank and Sammy, on the break-up of their marriages, croon "In the Wee, Small Hours of the Morning" or "What Kind of Fool Am I?". Moreover, Martin's destructive drinking hardly compares with Sinatra's involvement in corruption and violence – the show brings up the old theory that JFK's assassination was a Mob hit, revenge for its contributions being followed by brother Bobby's crackdown on crime. And Davis's troubles in a still-segregated America are hardly discreditable, nor are they revelations. I'm no rat-pack or Kennedy buff, but, apart from the charge that Sinatra was a bad man for Lucky Luciano, I found the material to be very old news.

As Bishop, Alan Rothwell does not look or act remotely like the morose Jewish hanger-on, and Robin Kingsland, stiff and charmless as Lawford, bizarrely doesn't even have an English accent. But Richard Shelton (Frank), Alex Giannini (Dean) and Peter Landi (Sammy – but why isn't a black actor playing this role?) give performances that, while poor imitations, work well at summing up the artists' flavour and appeal.

Apart, however, from a moment in which Sammy's wife tells him she's leaving because he spends more time with the boys than with his family, Rat Pack Confidential never tackles what makes this group of men seem so distasteful today – its assumption that the admiration and envy of other men is far more valuable than the love of women and children. For this, as well as the hero-worship that finally overcomes the harshness, this show really ought to be called "Rat Pack Sentimental".

To 21 Sep (0115-941 9419)