On the fifteenth anniversary of 9/11, I went to see two classical Greek tragedies about the toll of war on the human psyche. General Joseph Dunford, Jr., the chairman of the Joint Chiefs of Staff and the highest-ranking officer in the U.S. Armed Forces, was in the audience at the National Geographic Society. So were a couple of hundred military officers and veterans, with their families. They were rapt when the Emmy-winning actor Reg E. Cathey wailed in agony onstage, as Ajax, a great Greek warrior overcome with guilt, madness, and suicidal rage during the ninth year of the Trojan War. In a blind fury, Ajax slayed all the cows and sheep around him, believing they were the commanders who had betrayed him and his honor. He turned his home into a blood-strewn slaughterhouse. When he came to, he was overcome with shame.

“When a man suffers without end in sight, and takes no pleasure in living his life, day by day wishing for death, he should not live out all his years,” Ajax moaned. Tears flowed down his cheeks—and the play was only a reading. Moments later, Cathey enacted Ajax’s suicide. “No more talk of tears,” Ajax said. “It’s time,” and he lunged onto his sharpened sword.

The ancient Greeks, who lived in the world’s first militarized democracy, at one point faced war on six fronts. They understood the toxic costs of conflict. Almost twenty-five hundred years ago, Sophocles, Aeschylus, and Euripides wrote tragedies about the human spirit shattered, corrupted, and abused by war. Sophocles, who was also a long-serving general, wrote “Ajax.” Catharsis was so integral to Greek military life that war tragedies were performed during annual theatre festivals for seventeen thousand troops, from lowly cadets to commanders, writes the author and director Bryan Doerries, in his 2015 book, “The Theater of War: What Ancient Greek Tragedies Can Teach Us Today.”

Since the attacks in 2001, more than 2.7 million Americans have been dispatched to conflicts in Afghanistan, Iraq, and, most recently, Syria, with smaller teams of Special Forces, trainers, advisers, and intelligence and logistics staff elsewhere in the Middle East, North Africa, and South Asia. More than half have done multiple tours—some as many as four or five stints. Combat missions are technically no longer being undertaken, even as the wars rage on; the United States plays mainly a support role now. Yet psychological casualties—what are known as “moral injuries”—are still soaring.

Sixty per cent of veterans from the most recent wars now suffer a mental-health issue related to their military service, according to a survey, in May, by the Iraq and Afghanistan Veterans of America. Forty per cent have contemplated suicide—at least once. Twenty veterans kill themselves every day, the Department of Veterans Affairs reported in July, from the first comprehensive study of military suicides. The study scoured fifty-five million veterans’ records, from 1979 to 2014. (Suicides among female veterans increased by eighty-five per cent over that period.) Those figures do not include suicides among active-duty soldiers, sailors, airmen, and marines, which began to increase in 2005.

To confront the epidemic of suicides, Doerries founded the Theater of War project, in 2008, based on his own translations of “Ajax” and “Philoctetes.” “I realized that if I didn’t do something, I was complicit in the betrayal of those who had gone to serve,” he told me.

At the 9/11 reading of the plays, David Strathairn, the Emmy-winning and Oscar-nominated actor, portrayed Philoctetes, an injured warrior abandoned on an island by his own forces. “Earth, swallow this body whole, receive me just as I am, for I can’t stand it any longer!” he screeched, pleading. The pain “cuts straight through me. I am being eaten alive.” He depended on “a special herb” to diminish his anguish.

“Oh, I am wretched!” he lamented. “Death! Death! Death! Where are you? Why, after all these years of calling, have you not appeared?” Unlike Ajax, Philoctetes was saved, after nine years of suffering, albeit mainly because his skills as an archer were needed for war.

The travelling Theater of War project has now put on more than three hundred and fifty performances—all for free—for current and former military personnel at U.S. military bases on three continents, as well as at firehouses, churches, college campuses, libraries, a homeless center for veterans in Long Island City, and even an outdoor theatre at Guantánamo Bay.

“The venues don’t matter,” Strathairn told me. “Here’s this little National Guard center in a suburban neighborhood, and it has folding chairs in a cold room. Very quickly, the room disappears. The space becomes about the people.”

It’s bare-bones, blunt-force theatre. “This approach is not for everyone,” Doerries said. “But it’s not coincidental that the most powerful generals in the land have taken hold of it.”

The project won early support from Brigadier General Loree Sutton, who was the highest-ranking mental-health professional in the U.S. military at the time, after the Walter Reed scandal, in 2007, revealed the shoddy treatment of wounded warriors. She proposed renting football stadiums so that audiences of thirty thousand could see the Sophocles plays. “Time is not our friend,” she told Doerries, seven years into the Iraq War. Doerries wanted an intimate setting; the plays are the catalyst for soldiers to vent their feelings in audience discussions.

The first performance was for four hundred marines in San Diego, in 2008. In the public discussion afterward, as Doerries recounted in his book, Marshéle Waddell told the audience, “I am a proud mother of a marine and the wife of a Navy SEAL. My husband went away four times to war, and each time he returned, like Ajax, dragging invisible bodies into the house. The war came home with him. And, to quote from the play, ‘Our home is a slaughterhouse.’ ”

Strathairn was there. “The real drama of the evening always begins when we finish the reading. The purest, most visceral phenomenon of dramatic exchange happens in the audience,” he told me. “What’s astounding is that people, having never come close to reading Greek literature, will hear this once and, in the talkbacks, quote things characters have said. It’s been seared into them.”

After one performance, he recalled, a young man delivered a card to the cast from a fellow-soldier whom he had brought to the performance. “The soldier had been entertaining that day, that week, thoughts of suicide,” Strathairn told me. The card said, “Thank you for saving my life.”

Cathey has done some hundred shows. “It’s fun to see a couple hundred marines come in and they’re looking around. ‘What is this Greek shit?’ ” he said. “And I smile to myself, because I know by the end they’ll be at the edge of their seats. And then they talk.”

“I remember this kid at Fort Riley. He was only twenty-four. He got up and talked about doing four tours in Iraq and Afghanistan. He said he couldn’t tell his wife that the reason he felt bad was because he really needed to kill someone—and then I saw all these heads around him nodding,” Cathey recalled. “The kid had started out as a rock-hard soldier, and then his friends died and he was upset. It felt good to him to kill people, and he knew that it was wrong and he was tormented, but he still wanted to do it. Then the kid said, ‘How do you explain this to the woman you love?’ ”