An offset rotary printing machine which includes a first printing cylinder and a second printing cylinder in which printing is performed on a web at a nip between the pair of printing cylinders, the second printing cylinder contacting the first printing cylinder and being shifted downstream from the first printing cylinder. The printing machine includes an angle adjustment mechanism for adjusting an angle of a plane connecting center axes of the pair of printing cylinders which is inclined to a plane perpendicular to the moving direction of the web, and a controller for controlling the angle adjustment mechanism, based on parameters interrelating to a delamination occurrence probability that is caused as printing is performed by the downstream second printing cylinder.