No one collects data on the number of veterans participating in medical-marijuana programs in the 17 states where it is legal. But veterans and program advocates say those who have served are turning to cannabis more and more to deal with the disabling symptoms of post-traumatic stress disorder, traumatic brain injuries and chronic physical pain.

An earlier version of this story included a statement about the prevalence of substance abuse among veterans, which was attributed to Dr. Edward Gogek, an addiction psychiatrist. His remark was in reference to veterans who are patients in VA hospitals, not the overall veteran population.