An underground explosion crests shock waves, which propagate to a buried structure through the이 ground. Due to the explosion, very high stresses and large deformation occur in the ground so that the shock waves decay gradually. In this study the numerical simulation of the ground shock attenuation has teen performed. One dimensional wave equation is presented and the finite difference method is applies. A Cap model is adopted to describe the stress-strain behavior of the ground. The results are expressed by the attenuation of the peak stress and the particle vrelocity by the time and the distance.