A method of superplastically forming a part over period of a forming cycle in which a blank of the material is provided and heated to within a certain range of temperatures. An analytical model is provided that determines locations of the blank that will deform most rapidly when forming pressure is applied. As the forming pressure is applied, the displacements are monitored at such locations while the blank is being deformed. The strain rate is then calculated and feedback control is provided to affect the strain rate at such locations that will reduce the tendency of the blank or part to cavitate.