It has never been considered especially cool to be a fan of Huey Lewis and the News. Even during its heyday in the 1980s, song and album titles such as “Hip to Be Square,” “Sports,” and “Fore!” — the last was a golf reference — summed up the image put forth by a group led by a man who looked like a shaving cream model, playing R&B-braised rock music that, while well-crafted, was often viewed as lacking the soul and spirit associated with those respective genres. 

Strangely, these shortcomings become assets of a sort in “The Heart of Rock and Roll,” the new show now bringing the group’s repertoire to Broadway. Jukebox musicals, for all their contemptible elements, can be most irritating when they try too hard either to deify an artist or to find fresh wit and relevance in a popular repertoire. One of the reasons “Mamma Mia” became an enduring hit is that it steered clear of both these strategies, choosing instead to have giddy fun with what happens to be one of the most inviting catalogs in pop music.

If the songs featured in “Heart” are less compelling — for me, at least — the approach is similar, and very much in line with the self-deprecating humor that has always, notwithstanding his square-jawed handsomeness, made Mr. Lewis seem more modest and appealing than many cooler rock stars.

The musical’s hero is Bobby, a young musician who, after 10 years of trying in vain to fulfill his own pop-star dreams, leaves his band and takes a job working for a cardboard box-making company. After a misguided entrepreneurial ploy gets him fired, he is undeterred, following the company’s owner, Stone — along with Stone’s lovely and charming daughter, Cassandra, who also works for the company — to a convention at Chicago; Bobby then proceeds against all odds to try to regain Stone’s trust, as Cassandra inevitably falls for him.

The book, by Jonathan A. Abrams (based on a story by Mr. Abrams and producer Tyler Mitchell), is unabashedly, almost defiantly goofy. A supporting character named Tucker, Cassandra’s old college beau, is a lanky cartoon villain who could have delivered comic relief in Oliver Stone’s “Wall Street” — the film provides a couple of the numerous Reagan-era pop culture references here — while Bobby’s three ex-bandmates suggest goofballs in a buddy flick.

Yet there are genuinely funny lines here, and under Gordon Greenberg’s joyful, vivacious direction, the actors sustain our interest and affection. Leading man Corey Cott sings robustly and lends an easy charm to Bobby, and his buff good looks make him a credible aspiring idol in Mr. Lewis’s mold.

McKenzie Kurtz is pleasingly pert as Cassandra, while veteran John Dossett makes Stone predictably endearing. Even Billy Harrigan Tighe’s preening, bullying Tucker earns our sympathy now and then; at one point, another supporting character, a Swedish furniture mogul played by a hilarious Orville Mendoza, notices him and asks, “Who is this Pez dispenser?”

At the preview I attended, though, the audience favorite was clearly Tamika Lawrence, who brings a big, shiny voice and sly comedic timing to the role of Bobby’s colleague and friend, Roz. The crowd also ate up Lorin Latarro’s splashy, exuberant choreography, and Nikiya Mathis’s hair, wig, and makeup design, which captures all the excesses of the era.

Of course, I’m sure that most of my fellow theatergoers were there to hear beloved chestnuts like the show’s title song as well as “The Power of Love,” “If This Is It,” and “Do You Believe In Love.” Even if you’re not an admirer, “The Heart of Rock and Roll” offers more zany grace and buoyancy than most of its peers.