Abstract: To discuss the effects of the damage criterion parameter form, research on numerical methods for the typical ring stiffened cylinder of underwater explosion was conducted in this paper with Autodyn. Three damage modes were calculated including the collapse deformation of the cylinder's part under blasting, the concave deformation in the middle of the cylinder and the fracture of the cylinder. By analyzing the relations between the damage modes and the damage criterion, the research shows that, basing on the criterion parameters of the shock wave overpressure, the specific impulse,the energy flux density and the damage degrees are different with different explosive charge. Especially, explosive charge has the greatest influence on the criterion parameters of the specific impulse. Finally, it is proposed that explosive charge power and the distance ratio are the general forms of the criterion parameters. This criterion parameter form is proved to be reasonable with power index obtained from the simulation results and the criterion parameter obtained with small explosive charge influence.