Abstract: Critical stress and inertial exponent are treated as two characteristic parameters for the asymmetric dynamic buckling of cylindrical shells under axial step loading.The supplementary restraint equation of buckling deformation at compressive wave front is derived by the use of the criterion of transformation and conservation of energy in the transient buckling process.The Galerkin method is used to solve the governing equations,and the algebraic eigenvalue problem including the two characteristic parameters is obtained.On condition that the supplementary restraint equation is satisfied,the solution of the eigenvalue problem gives the values of the critical stress and the inertial exponent for the dynamic buckling.