In order to study the characteristics of blast in geotechnical materials,the material behavior of power-hardening solid was investigated by the elliptic-equation yield criteria and self-similar hypothesis with a Hopkins three region model.First,by studying elastic region,the stress distribution and the continuous conditions in the intersection of plastic and elastic areas were given.Then the nonlinear differential equations to solve the problem of dynamic expansion in the plastic zone were deduced.At last,numerical solutions of the non-linear differential equations which meet with the given boundary conditions were obtained by shooting method,the effects of material parameters on the stress-strain fields were also discussed.Result shows that the elliptic-equation yield criteria can discribe the dynamic expansion of spherical cavity in pressure-sensitive medium.