“The Sound of Music” tour at the Kennedy Center’s Opera House arrives not from Broadway, where this production has never been, but from the road, where it was launched in 2015. It’s been well-reviewed across the country, and you can see why. Jack O’Brien’s conspicuously traditional staging is deeply respectful of what is probably the most beloved of the Rodgers and Hammerstein musicals.

Reverent is the word, even if O’Brien breaks a bit with how he sees the plucky postulant-turned-governess Maria and the forbidding Captain Georg von Trapp. (Julie who? Christopher who?) The show revels in its abbey scenes; multiple Tony Award-winning lighting designer Natasha Katz casts divine shafts on the proceedings, as if heaven itself is blessing events. It’s an act of faith.

The devotion extends to the humble yet beaming portrayals of Maria and the Captain. O’Brien, a particularly rangy Tony winner (“Hairspray,” the Tom Stoppard trilogy “The Coast of Utopia”) thoroughly scrapes the fingerprints off the stars who played these characters in the movie, starting with Charlotte Maltby’s athletic Maria. The tall Maltby, daughter of writer-director Richard Maltby Jr. (“Ain’t Misbehavin’”), oozes robust health; at a glance you suspect she could scamper across the Alps, yodeling over the peaks. She’s gangly and fun with the seven von Trapp children — a superbly disciplined, winsome litter — so we like her.

Maltby’s bright, clear voice has a steeliness that stops just shy of being too Broadway brassy. She’s a girl next door who belongs outdoors; she never had a chance in the abbey.

Nicholas Rodriguez’s von Trapp, meanwhile, really isn’t scary in the least. Rodriguez has been working his way through the Rodgers and Hammerstein leading men, and there is a boyishness about his presence and lyrical singing that made him more convincing as a laconic Curly in “Oklahoma!” than as the shadowy Billy Bigelow in “Carousel” (both at Arena Stage). He’s a gentle von Trapp, and naturally radiant — not what you’re expecting.

Nicholas Rodriguez and Charlotte Maltby in “The Sound of Music.” (Jeremy Daniel)

Rodriguez’s von Trapp softens easily and plainly belongs more with Maltby’s open Maria than with Teri Hansen’s pragmatic Elsa, the businesswoman poised to marry the widowed von Trapp. That saps the show of romantic intrigue, and what passes between Rodriguez and Maltby isn’t quite chemistry, despite kisses so demonstrative that kids in the audience giggle. But it makes sense that this fundamentally musical man would glow when he finally sings, which the golden-throated Rodriguez does with ample wattage.

The kids are the soul of the show, which is perhaps the ultimate family musical. (For the record, the cute brood is played by Paige Silvester, Elliot Weaver, Stephanie DiFiore, James Bernard, Dakota Riley Quackenbush, Taylor Coleman and Anika Lore Hatch, with Austin Colby on the edges as Liesl’s beau Rolf.) The movie reorganized the songs so that Maria sang “My Favorite Things” to soothe the children in a storm, but in the stage version it’s “The Lonely Goatherd.” (“My Favorite Things” comes early, with the sympathetic Mother Abbess.) Like “Do-Re-Mi,” the number makes you grin: the energy cycles up smoothly, almost naturally, and the singing is lovely.

I have mixed feelings about the old-fashioned painted scenery of Douglas W. Schmidt’s set, but not about Jane Greenwood’s flavorful period costumes. The rest of the ingredients add up, from Merwin Foard’s squishy dinner guest-impresario-Nazi accommodationist Max Detweiler to Melody Betts’s suitably anthemic rendition of “Climb Ev’ry Mountain” and the sensitive playing by the orchestra. It’s not a put-it-in-the-pantheon “Sound of Music,” but fans and newcomers alike should find themselves settling in comfortably with this patient, confident show.

The Sound of Music book by Howard Lindsay and Russel Crouse, music by Richard Rodgers, lyrics by Oscar Hammerstein II. Directed by Jack O’Brien. Choreography, Danny Mefford; sound design, Ken Travis. Through July 16 at the Kennedy Center’s Opera House. Tickets $39-$149. Call 202-467-4600 or visit kennedy-center.org.