The diffusion wave and incident wave stress fields of simple harmonic wave propagation in viscoelastic media with Kelvin model are presented. The propagating wave is divided into two parts of diffusion wave and incident wave. The diffusion wave and incident wave stress fields in elastic media are deduced firstly. Then the diffusion wave and incident wave stress fields in viscoelastic media with Kelvin model are presented combining elastic wave theory and viscoelastic theory. And the deduced stress fields can be expressed with the displacement and velocity expressions of diffusion wave and incident wave. The results are propitious for application of wave theory to viscoelastic media