Wave propagation in unbounded domains has attracted a lot of attentions in engineering field. Surface waves in off-shore structures or dams, radio waves or elastic waves caused by blasts are just some examples of applications, of which the latter is focused by structural engineers. Several attempts have been made to solve this problem. Here some of the solution methods are briefly reviewed and one of them which is based on finite element method (FEM) is discussed. It seems that one of the error sources in this method is the shape and arrangement of the elements. To avoid this error, we studied meshless techniques such as finite difference method (FDM) and finite point method (FPM) and results of this new meshless method have been compared with the original method. It has been observed that FDM can only solve scalar wave problem. On the other hand, FPM is capable of solving both types of wave problems, while the results are still affected by pollution error as in the original method using FEM.
