In this paper a computational method is presented to solve the plane problem of wave propagation in linear-elastic plate with zones of different materials. An existing numerical scheme of bicharacteristics for rectangular plate is extended to plates with curvilinear boundaries. In order to show the validity of the employed concept, it is necessary to examine the numerical results whether they reproduce the well-known physical phenomena of stress waves. It seems also desirable to make a comparison between the numerical results and appropriate experimental results for plates with curvilinear boundaries. Also studied are the focusing phenomena induced by reflection and refraction at curved outer boundaries and material interfaces.