In this project, we are interested in solving wave like equations and systems by using Hyperbolic Function Method. The method is used to construct periodic and solitary wave solutions for some nonlinear wave type equations and systems such as the nonlinear Klien Gordon equation, Sinh-Gordon equation, Sin-Gordon equation, Telegraph equation and a system of Klein-Gordon-Zakharov (KGZ) equations. The main advantage of this method is that it can be applied directly to most types of differential equations. Furthermore, the method is capable of greatly reducing the size of computational work