Simulation of free surface flow has been an interesting area of research for many years. Various methods and computational algorithms have been developed, so far. In this paper, a numerical model for the two dimensional simulation of free surface motion is presented. The model which is based on a smoothed particle hydrodynamics method is used to solve the Navier - Stokes equation and the free surface flow. Two different smoothing kernels are also implemented in the simulation and compared with each other. The numerical model is also verified by comparing the obtained results against the documented experimental and numerical findings. Relatively good agreement is displayed in the verification phase.