A synchronous rotary cross cutter for cutting a material web of paper or the like has two drums which synchronously rotate about parallel axes at opposite sides of the material web, and a cutting element on each drum. One of the cutting elements is elastically yieldable, and the drum for this cutting element has a helical bearing surface with an axis lying on the cutting edge of the elastically yieldable cutting element. The helical surface of the drum has such an inclination that the free angles of the elastically yieldable cutting element at the beginning and at the end of the cutting line are identical.