Four decades after the publication of the concept of Engel’s “biopsychosocial model” for medicine, and its subsequent enthusiastic embrace by psychiatry, it is widely accepted as a valid alternative to the reductionism of biological psychiatry. However, unlike models in mainstream science, the original model has not been developed or expanded. Despite widespread efforts to “talk it up,” Engel’s “biopsychosocial model” has failed to have any lasting impact on psychiatry. The reason is simply that it doesn’t exist. The logical flaws in Engel’s original concept are explored, and some consequences noted.