The story goes that Norman Rockwell, seeking authenticity, wanted to rip holes in the soldiers’s shirt. The GI said fine. Rockwell asked to smear mud on his face and hands. Not a problem.

But when the artist asked to rub dirt on his machine gun, the soldier refused: No proper gunner could tolerate that. So Rockwell portrayed the GI as tattered and begrimed, but with his big gray Browning machine gun sleek and clean.

This rare and meticulous World War II painting, by an artist whose work routinely fetches tens of millions of dollars, hangs not in a museum or gallery, but in a state-of-the-art Army conservation center at Fort Belvoir.

It is part of the Army’s extensive collection of military art — much of it by renowned painters and illustrators — that is ready and waiting for the future National Museum of the United States Army.

But the museum, which has been a decade in the making, is at least four years from opening and has less than half the money it needs for its construction, according to its chief fundraiser, Creighton W. Abrams Jr., a retired brigadier general.

The Army Historical Foundation, which he directs, has raised $76 million of the $175 million it needs. Abrams said he expects the museum to open in 2018, at the earliest. It is also to be located at Fort Belvoir, six miles west of Mount Vernon.

The project, like many such endeavors in the Washington area, has been blessed with generous donors, slowed by years of planning starts and stops, and hampered by the ups and downs of fundraising.

In 2010, fundraising was good, Abrams said in an interview last week. It was not as good in 2011, worse in 2012, but better in 2013. “We raised $10 million last year,” he said. “And we think we’re going to get between $15 [million] and $20 [million] this year.”

Meanwhile, the art collection and a trove of other Army historical treasures wait in climate-controlled seclusion.

The collection is superb.

It has four original works by Rockwell, and several by the noted World War II illustrator Tom Lea — including his famous portrait of a stunned, battle-fatigued Marine, entitled “Marines Call It That 2,000-Yard Stare.”

There’s art by Floyd MacMillan Davis, the magazine and advertising illustrator, and by Edward Reep, who, on the ground, painted the World War II bombing of Italy’s Monte Cassino while it was still underway.

Visitors and officials examine some of the artwork during a tour of the U.S. Army's art collection at Ft. Belvoir. (Bill O'Leary/The Washington Post)

“The earth trembled (and so did my hand),” Reep said later.

There’s a series of elegant 1840s paintings from the Mexican War by James Walker, portraits of Civil War Gen. Philip Sheridan and President Abraham Lincoln, and stark, impressionist works from the Vietnam War.

In all, there are 16,000 pieces of art stored in the Army’s $24 million Museum Support Center, which was created to care for items destined for the museum. Though construction of the museum was delayed, that of the lower-profile support center was not.

The art had been housed in the leased basement of an office building in downtown Washington until it was moved to the center in 2010, according to Sarah G. Forgey, curator of the art collection

At the new site, in a spare, cavernous room, multiple paintings are hung on giant sliding wire screens that can be recessed for storage or pulled out for examination.

Although American martial art became well known during the Civil War, with such painters as Winslow Homer and Conrad Wise Chapman, and illustrators like Alfred Waud, the official War Department art program began in World War I, Forgey said.

The department sent eight artists to France, commissioned as captains in the Corps of Engineers.

They produced about 500 pieces which, after the war, went to the Smithsonian Institution because the Army had no place to keep them, Forgey said.

That collection is still there. Asked if it can be retrieved, she said, “that remains to be seen. . . . It’s in good hands.”

When World War II began, the government set up the War Art Advisory Committee, which selected 42 civilian and military artists to cover the conflict.

The committee chairman was the Philadelphia lawyer-turned-artist George Biddle.

“Any subject is in order,” he told the selectees.

“Battle scenes and the front line . . . the dying and the dead; prisoners of war . . . wrecked habitations . . . the nobility . . . cruelty, boredom of war. . . . You may be guided by Blake’s mysticism, by Goya’s cynicism. . . . Delacroix’s romanticism. . .”

Three months into the project, Congress cut its funding.

But Life magazine, which had its own artists in the field, picked up many of the program’s civilian artists, and the work continued, Forgey said during a tour of the collection last week.

In 1960, Life donated 1,050 originals to the Defense Department.

There was a vast array of work.

Floyd Davis produced “GI Perfume Shop,” a humorous image of a rumpled soldier and a well-dressed French saleswoman in her perfume store.

Forgey said Davis later explained the painting: “He said the line was . . . across the street with everybody trying to buy the cheap perfume and bring it home to their sweethearts.”

Davis also painted the grim “GIs in Paris,” which shows three battered, unshaven and utterly exhausted American soldiers in 1944. “They look woebegone,” Forgey said, “like they’ve been to hell and back.”

And he painted “Coffins at Nazi Execution Place,” which depicts four empty wooden coffins each containing shreds of victims’ clothing, and three execution posts out a window in the background.

The painting was reproduced in Life in July 1945, with a caption that read, in part: “Torture chamber, where Nazis murdered Parisian patriots. . . . Victims were tied to posts . . . shot.”

Tom Lea spent time in the Pacific theater.

He painted the staring Marine against the backdrop of the fierce battle for the island of Peleliu, where he had gone ashore with the Marines in 1944.

Almost 1,800 Americans and about 10,000 Japanese were killed there.

Another of Lea’s Peleliu paintings, “The Price,” shows a wounded Marine running with his left arm, shoulder and face bloody and shredded. Lea witnessed the scene, couldn’t forget it and later painted it in a studio, Forgey said.

The Army collection also includes work by World War II artists sponsored by Abbott Laboratories that focused on the medical and health aspects of the conflict.

One striking work depicts Allied soldiers recovering in a makeshift hospital in Naples, Italy, with a huge fascist mural on a wall in the background.

Forgey said there was no official Army art program during the Korean War, but one was reestablished during the Vietnam War, with 10 teams of four or five artists each.

They produced eerie images in vibrant colors of downed helicopters, flaming structures, and works like Roger Blum’s spooky “Patrol in the Jungle.” The painting captures wary soldiers plodding through a swamp that seems to engulf them in blue-green gloom.

“The Vietnam period, the artwork’s very immediate,” Forgey said. “You really do feel like you’re right there.”

More recent conflicts have produced work in tans, browns and grays, from the deserts of Iraq and the mountains of Afghanistan.

As for Norman Rockwell, his machine gunner painting was designed as a war poster called “Let’s Give Him Enough and On Time,” about the need for war materiel.

Forgey, the curator, said she did not know the name of the soldier who posed, torn and grimy, in Rockwell’s Vermont studio in 1942, and she could not say if he went on to survive in the real war.