The dynamic spherical cavity expansion with damage and elastic area was investigated when distortion is so small that no plastic area arisen. First, by study of elastic region and initial damage, the stress distribution and the continuous conditions in the intersection of damage and elastic regions were given. Then the governing equations to solve the problem of dynamic expansion in the damage zone were deduced. Finally, numerical solutions of the non-linear differential equations were obtained by shooting method. The results show that some material parameters such as v、n、m have influence on the field quantities of elastic and damage regions.