Abstract: Taking cavity expansion in an elastic medium as the object of study, using the theory that movement fields on the boundary conditions of velocity and stress have the same potential, applying Laplace transformation and its convolution theorem, transformation between two boundary conditions was obtained, and transformation between velocity field and stress field of the spherical wave was got. Taking a double-exponential decay of dynamic stress and a sine exponential decay of velocity for examples, characteristics of the movement field in the spherical wave were analyzed. Results show that there does not lie a simply linear relationship between the stress and velocity in the spherical wave. Compared with the plane wave, the particle velocity in the spherical wave is smaller. Critical factors resulting in these differences are the wave propagation distance and wave velocity in media, the smaller the wave propagation distance is and the bigger wave velocity in media is, the more distinct these differences are.