Stock was trained at the University of Minnesota, completing a surgical internship and residency before coming to UCSF for a transplant fellowship. He joined the UCSF faculty in 1992. Stock is an active teacher and supervises surgical residents and fellows. He is a member of numerous professional and honorary societies. In his research, he studies the mechanisms of allograft rejection, chimerism (anti-rejection therapy using the donor's bone marrow cells) and pancreatic islet cell transplantation.