Watching Disney’s live-action adaptation of its animated classic “Dumbo,” one can truly believe an elephant can fly.

The harder trick, the one moviegoers always hope will happen and rarely does, is that director Tim Burton (“Beetlejuice,” “Sweeney Todd” and others) can stick the landing on one of his visually wondrous but narratively spotty movies.

This time, backed by a script by blockbuster maven Ehren Kruger (who has worked on three “Transformers” movies and “Scream 3”), Burton comes closer than usual to getting it right, but it’s still a mess.

Set in 1919, the story begins in the Medici Brothers Circus, a rundown collection of acts touring the country by train. (Yes, animated fans, the engine is the Casey Jr. — one of the many icons from the 1941 original.) When the tour gets to Joplin, Mo., circus kids Milly (Nico Parker) and Joe (Finley Hobbins) get a surprise at the train station: Their father, Holt (Colin Farrell), finally back from World War I, with a chest full of medals and a missing left arm.

Holt and his wife, Annie, used to be the roping-and-riding stars of the Medici circus. But while Holt was in Europe, explains gruff circus owner Max Medici (Danny DeVito), Annie died of influenza and the horses were sold off. The only job left for Holt is to tend the troupe’s elephants, including Max’s latest acquisition, Mrs. Jumbo, who’s about to have a baby.

Max hopes the baby elephant will be his new star attraction — but when he sees the newborn and his giant ears, Max fears the animal will never be circus-worthy. But Milly and Joe have faith, and they see that when the baby, dubbed Dumbo, grabs a feather, it allows him to go airborne. Soon that’s incorporated into an act, and the Medici circus is suddenly successful again.

That’s where the 1941 movie ended, but here the story is just kicking into gear. Dumbo’s flying prowess gets the attention of entertainment mogul V.A. Vandevere (Michael Keaton), who wants to buy Dumbo off of Max — or, when that fails, hire the whole circus to join his New York theme park, Dreamland. What’s more, Vandevere aims to pair Dumbo with his star trapeze artist, “queen of the heavens” Collette Marchant (Eva Green).

Burton creates some gorgeous interpretations of the animated movie’s most famous scenes, from Dumbo’s clown act to the “Pink Elephants on Parade,” while throwing in some Busby Berkeley touches in the Dreamland circus extravaganza. Burton and Kruger reference some of the original’s problematic moments — the alcohol references, or the outdated Jim Crow stereotyping — in clever and inoffensive ways. And, yes, the song “Baby Mine” (heard twice in the film, the second time covered by Arcade Fire) can still make grown men cry.

And where the 1941 version was an animal-driven story, this take is centered mainly on the humans — a tale of families, biological and manufactured, bonding together in the face of capitalist greed.

If only Burton could make all the components mesh. Farrell and the kid actors seem to be making a sensitive family drama with computer-animated elephants; Green is in a smoldering film noir; and DeVito and Alan Arkin (as Vandevere’s main investor) are doing Borscht Belt comedy. Meanwhile, Keaton — who is reuniting with Burton for the first time since “Batman Returns” (which also starred DeVito) — is off in his own villainous orbit, fun to watch but miles apart from everything else that’s going on.

For all the moments of splendor, there are also moments of idiotic excess (the biggest perhaps the cameo by boxing announcer Michael Ruffer) that undercut the magic Burton is trying to conjure. “Dumbo” gets airborne, but it’s another bumpy flight for a director whose reach so often extends his grasp.

——

★★1/2

‘Dumbo’

Disney’s animated elephant flies again, in a live-action adaptation loaded with visual delights but a clunky human-focused narrative.

  • Where • Theaters everywhere.
  • When • Friday, March 29.
  • Rated • PG for peril/action, some thematic elements, and brief mild language.
  • Running time • 112 minutes.