The deformation of dynamic damage in a pressure-sensitivity media was investigated by means of spherical cavity expansion model. By constructing a three region model of spherical cavity, dynamic solutions with damage and elastic area was investigated when distortion was so small that no plastic area arisen (cavity expansion rate is generally less than 0.4). Firstly, by elastic and damage mechanics, the continuous conditions in the damage region were given. Secondly, the governing equations and analytical solutions of the damage region were deduced. Finally, numerical solutions were obtained by shooting method. The result shows that some material parameters such as damage index and Poisson ratio have significant effects on the range and field quantities of damage region.