We propose a coupled model to simulate shallow water waves induced by elastic deformations in the bed topography. The governing equations consist of the depth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatics formulation for the bed deformation. The perturbation on the free-surface is assumed to be caused by a sudden change in the bottom beds. At the interface between the water flow and the bed topography, transfer conditions are implemented. Here, the hydrostatic pressure and friction forces are considered for the elastostatic equations whereas bathymetric forces are accounted for in the shallow water equations. The focus in the present study is on the development of a simple and accurate representation of the interaction between water waves and bed deformations in order to simulate practical shallow water flows without relying on complex partial differential equations with free boundary conditions. The effects of location and magnitude of the deformation on the flow fields and free-surface waves are investigated in details. Numerical simulations are carried out for several test examples on shallow water waves induced by sudden changes in the bed. The proposed computational model has been found to be feasible and satisfactory.