When the wave approaches to coast, the wave steepness, which is the ratio of wave height to water depth increases due to depth re-duction. This increase continues to a certain extent, until finally at this limit, the wave breaks. Wave breaking results in the releasing of wave energy, production of coastal currents and increase of the average water elevation. The surf zone and swash zone is the most active region from the aspect of hydrodynamic processes. In this region sediment transport and seabed changes are due to the breaking waves and its induced nearshore currents. Numerical models based on the Navier-Stokes equations can model the flow field very accurately. The generation, transformation and dissipation of turbulence can be delicately modeled by closuring a proper turbulence model to the main model. Besides the free surface shape can be estimated using an appropriate numerical algorithm. As a final remark it can be concluded that numerical modeling can accurately model wave breaking. The main objective of this research is to define the wave breaking in shallow water and describing the relevant hydrodynamic processes such as wave run up, generation and dissipation of turbulence. In this paper, a two-dimensional numerical model has been developed to study wave breaking and wave run up on a sloping beach. The model is based on solving the Reynolds Averaged Navier-Stokes (RANS) equations, and a k-e turbulence closure model. The free surface is tracked by the VOF technique; the log-law profile for the mean velocity is applied at the bottom. Propagation, deformation, breaking and overturning of an Airy wave have been numerically studied with the main emphasis on velocity and turbulence characteristics.