While investigating the Tsunami wave project, a numerical method was devised to solve the initial boundary value problem for the equations of the non-linear shallow water theory. The case of one horizontal dimension was considered in a domain bounded by a shore at one end, with the motion of the shoreline taken into account. In addition, this method enabled the incident wave to be introduced at the seaward end of the domain. The water was assumed to be at rest in the domain until the incident wave arrived, and the bottom was assumed to slope uniformly.