Jared Nepute plays Johnny in ’American Idiot,’ now at National Theatre. (Jeremy Daniel)

The touring company of “American Idiot” has already played two dozen cities this year, some of them one-nighters in places such as Manhattan, Kan., and Elmira, N.Y. That grind didn’t stop the young, non-Equity cast from bouncing and belting their hearts out Tuesday night at the National Theatre, where the show gets a mild break from the road through this Sunday, before trekking north and east for four more one-nighters next week.

You could hear the cast whooping behind the curtain before and after the performance, psyching themselves up and then blowing off steam. Still, the 90-minute rock opera adapted for Broadway from Green Day’s 2004 album feels less than electric.

The cast, full of recent college grads making tour debuts, is competent but rarely commanding in a show that tells its anxiety-of-youth-and-war story almost entirely through Green Day songs. The characters exist in the music, rendered by a five-piece rock band playing in front of the large scaffolding set that’s peppered with about two dozen flickering video screens.

The guitar-driven songs are grandchildren of buzzy, crunching anthems from the Who and the Clash, and director Michael Mayer (“Spring Awakening”), who co-wrote the book with Green Day’s Billie Joe Armstrong, steers this music as clear as he can from Broadway schmaltz. He sticks to the songs in the show’s post-9/11 scenario, which follows three disaffected young men through trials of sex, hard drugs (disturbingly depicted in action, choreography and on screens) and combat.

It’s a fat-free show, for sure — fast and loud and exploding with power chords and strobe lights. Steven Hoggett’s mosh-pit choreography is full of loose-limbed thrashes and twitches, and if familiar songs like the title tune and “Holiday” don’t quite set the house ablaze, at least they’re not insipid Broadway knockoffs. The reflective “Boulevard of Broken Dreams” and “Wake Me Up When September Ends” come off well, as do the sweeping “Quadrophenia”/“Tommy”-like suites that surely whispered “stage version!” in Mayer’s head.

The National Theatre presents the musical “American Idiot,” based on Green Day’s multi-platinum album. The hits featured include “21 Guns,” “Boulevard of Broken Dreams” and more. (Winyan Soo Hoo/The Washington Post)

Still, it never feels entirely like its own thing. The psychodrama “Tommy” and the anti-war “Hair” loom large, even if the “Idiot” tone is looser and grimmer, something reflected in the dark glowing set by Christine Jones and in the anti-hip clothes by costume designer Andrea Lauer. But a Green Day fan base is more substantial than most theater audiences, and buffs will have their own highly refined reasons for loving it or hating it. (It was famously blessed by Armstrong and even Melissa Etheridge, who each played the drug-dealing St. Jimmy at various times during the New York run.)

They’ve probably already made up their minds, since the musical debuted on Broadway in 2010 and lasted just over a year, with Tony Awards going to the rock-show efforts by Jones and lighting designer Kevin Adams. And on it goes: According to the show’s Web site, the “American Idiot” tour barnstorms 38 more North American cities at least through May.

American Idiot

Music by Green Day, lyrics by Billie Joe Armstrong, book by Billie Joe Armstrong and Michael Mayer. Directed by Michael Mayer. Sound design, ACME Sound Partners; video/projection design, Darrel Maloney. With Jared Nepute, Dan Tracy, Casey O’Farrell, Olivia Puckett, Taylor Jones, Mariah MacFarlane, Carson Higgins, Alex Boniello, Liam Fennecken, Sean Garner, Francesca Granell, Antwaun Holley, Andrew Humann, Alison Morooney, Johnny Newcombe, Michael Pilato, Eric Presnall, Turner Rouse, Jr., Josephine Spada and Chelsea Turbin. About 90 minutes. Through Sunday at the National Theatre, 1321 Pennsylvania Ave. NW. Tickets $48-$98, subject to change. Call 800-514-3849 or visit www.thenationaldc.org.