“The first time I heard Ajax’s speech, it knocked me back in my chair,” said Jeff Hall, a retired Army commander from Oklahoma who struggled with depression and suicidal thoughts after returning from Iraq. “It was me. I could see how he was betrayed in the text.”

Mr. Hall’s wife, Sheri, is the voice of Tecmessa in the video — the long-suffering spouse of Ajax, who lives in fear of her husband’s dark thoughts.

“She was walking around on eggshells and so were we during our time of Jeff’s PTSD onset, and the things going on with his anger and his depression,” she said. “It really spoke to me, especially with what she was dealing with. I was going through the same things.”

While Sophocles is better remembered for writing “Antigone” and “Oedipus Rex,” he was also a general in the Athenian Army and lived during the decades-long Peloponnesian War. He wrote “Ajax” and “Philoctetes” for audiences that most likely included his army’s own soldiers.

“The theme that’s most prevalent in both plays is betrayal. And betrayal, I’d argue and many others have argued, is the wound that cuts the deepest,” said Mr. Doerries, who wrote a memoir about the creation of his company called “Theater of War: What Ancient Greek Tragedies Can Teach Us Today.”

Theater directors typically look for new material or new venues. Mr. Doerries has made a specialty of seeking out new audiences for ancient texts. He mounted a reading of the Book of Job for people affected by Hurricane Sandy, Hurricane Katrina and the Fukushima nuclear accident and has done versions of “Prometheus Bound” for prison guards, including those at Guantánamo Bay.

But most of his work involves Sophocles and American veterans. In addition to his memoir, he has published his translations of Greek tragedies and even wrote a graphic novel about a United States Marine based on the story of Odysseus. He was recently named the public artist in residence by the New York City Department of Cultural Affairs and the Department of Veterans’ Services. This weekend, he’s hosting another Theater of War event in New York at the Intrepid Sea, Air & Space Museum.