The erosion of contact material is one of the critical failure mechanisms in switch devices. Thus it is important to study the characteristics of contact erosion. In this paper, a two-dimensional magnetic hydrodynamics (MHD) is established to get physical characteristics of the molten pool. The influence of the electromagnetic force, surface tension, buoyancy and Joule heating are considered in the model. The computed melting pool temperature distribution is then used together with the fundamental principles of gas dynamics and statistical methods for the calculation of the vaporization rates and sputter rates. The vaporization rates due to pressure gradient are obtained by using the equations of conservation of mass, momentum and translational kinetic energy across the Knudsen layer and adjacent regions. The sputter probability is determined by three essential parameters including size, shape and temperature of the melting pool. The deformation of the geometry is calculated using the volume of fraction method (VOF). According to simulation results, contact surface temperature, melting pool flow velocity and erosion rate are increased with the increase in arc current. The results also show that the Marangoni stress (the gradient of the surface tension with respect to the surface temperature) plays a major role in melting pool flow.