Incompressible Free Surface Flows One of the most powerful methods to implement the free surface is the Volume of Fluid (VOF) in this study, an algorithm is developed, which includes an implicit pressure based method (SIMPLE) with a staggered grid and a Lagrangian propagation VOF method. Based on this algorithm, a computer code is generated and a cavity with a free surface and two test cases of dam-breaking problems are examined and, then, the effect of fluid sloshing on a near wall is also analyzed and a time history of the normal force on the wall is presented. The results show good agreement with experimental and other computational results