But others disagreed, saying the program was desperately needed. And in the interview, General Casey said the mental effects of repeated deployments  rising suicide rates in the Army, mild traumatic brain injuries, post-traumatic stress  had convinced commanders “that we need a program that gives soldiers and their families better ways to cope.”

The general agreed to the interview after The New York Times learned of the program from Dr. Martin E. P. Seligman, chairman of the University of Pennsylvania Positive Psychology Center, who has been consulting with the Pentagon.

In recent studies, psychologists at Penn and elsewhere have found that the techniques can reduce mental distress in some children and teenagers. But outside experts cautioned that the Army program was more an experiment than a proven solution.

“It’s important to be clear that there’s no evidence that any program makes soldiers more resilient,” said George A. Bonanno, a psychologist at Columbia University. But he and others said the program could settle one of the most important questions in psychology: whether mental toughness can be taught in the classroom.

“These are skills that apply broadly, they’re things people use throughout life, and what we’ve done is adapt them for soldiers,” said Karen Reivich, a psychologist at Penn, who is helping the Army carry out the program.

At the training session, given at a hotel near the university, 48 sergeants in full fatigues and boots sat at desks, took notes, play-acted, and wisecracked as psychologists taught them about mental fitness. In one role-playing exercise, Sgt. First Class James Cole of Fort Riley, Kan., and a classmate acted out Sergeant Cole’s thinking in response to an order late in the day to have his exhausted men do one last difficult assignment.

“Why is he tasking us again for this job?” the classmate asked. “It’s not fair.”

“Well, maybe,” Sergeant Cole responded. “Or maybe he’s hitting us because he knows we’re more reliable.”