Nonlinear phenomena play a crucial role in applied mathematics and engineering, especially vibration problems. The theory of nonlinear problems has, recently, undergone many studies. Various approximation methods have been used for complex equations. In this paper, authors used reconstruction of variational iteration method to study the two types of waves equations including one–dimensional wave equation, kinematic wave equation and non-linear homogeneous wave equations. This new method which is based on Laplace transform has high rapid convergence and reduces the size of calculations using only few terms, so many linear and nonlinear equations can be solved by this method. The plots and tables show excellent agreement between our results and exact solution that represents the mentioned method can be used for a wide range of engineering problems.

nonlinear problem, approximate solution, analytical method, waves equation.