“American Sniper” joins the earlier “Zero Dark Thirty” and “The Hurt Locker” as one of the most incisive military dramas of the post-9/11 era.

Clint Eastwood, the 84-year-old Oscar-winning director of “Unforgiven” and “Million Dollar Baby,” helms the film, a tense, action-filled story of war abroad and trouble at home, with an unflinching hand.

In this biopic about Chris Kyle, the Navy SEAL who became the most effective sniper in U.S. military history, Kyle’s stateside struggles combine with the vexing urban warfare he wages during four deployments to Iraq. It’s powerfully unsettling cinema.

Kyle’s boots are big ones to fill. Bradley Cooper grew a beard for the part, beefed up his physique and tuned his speech to a Texas accent.

Kyle is a commanding character in the film — dubbed “The Legend” by his peers — but he’s no glory seeker. Instead, he humbly deflects praise. Because showboating isn’t Kyle’s way, Cooper expresses the sharpshooter’s inner qualities — courage, loyalty to brothers in arms, and dedication to duty.

Like a cowboy hero in a classic Western, Kyle is the archetypal good guy. Kyle’s vision of himself, illustrated in early “American Sniper” scenes, stems from childhood. His father explained life in the simplest terms.

“There are three types of people,” the elder Kyle tells his oldest son at the family dinner table. “Sheep, wolves and sheepdogs.”

Installed in various sniper perches, Kyle, the vigilant sheepdog, protects his comrades. In the tightly coiled urban warfare environment, he saves scores of Americans from the men, women and children who would kill them.

Kyle’s enemies realize how effective he is. They also give him a title — “The Devil of Ramadi” — and they put a bounty on his head. A taut rivalry develops between Kyle and a similarly skilled Syrian sharpshooter who sees Kyle as a prize kill.

For “American Sniper,” Eastwood and cinematographer Tom Stern create an immersive, battlescape experience. Handheld as well as fixed cameras positioned throughout sets capture the action from many angles. It’s frantic and alarming.

Following other war movies of recent vintage, “American Sniper” also has visceral impact. When Kyle’s comrades are struck down, the shock and tragedy of their misfortune strike home. In addition to how realistic the footage is, the film’s screenplay, written by Jason Hall and based in part on Kyle’s best-selling autobiography, reveals supporting characters to a degree that moviegoers can care about them. And post-battle hospital scenes don’t hide the damage done.

In reality, Kyle was wounded multiple times but, compared to his mangled peers, his body is relatively unscathed. In due course, though, he suffers psychological injuries.

Initially, Cooper gives two performances as Kyle. He’s the focused sniper on a mission he believes in. He’s also an ill-at-ease stateside soldier who denies he’s experiencing post-traumatic stress disorder.

Sienna Miller co-stars as Kyle’s wife, Taya. Kyle and Taya meet and court, like normal couples do and, on the same day that Kyle’s SEAL unit is ordered to deploy to Iraq, they marry. As emotional as it is to see Kyle’s peers in war slain and scarred, the scenes with Kyle and Taya become the movie’s pounding heartbeat. During one of her husband’s trips home, the exasperated Taya tells him that, even when he is home, he keeps his distance from his family. Miller’s wrenching performance as the warrior’s wife is among the most shattering work in the films of 2014.

“American Sniper,” a superbly staged and played military drama, doesn’t hold its shots. In equal parts, it’s an engrossing action-drama and moving, tragic story of a real hero.