Numerical simulation of multi material or multi-phase flows are one of the most challenging problems between computational fluid dynamics researches. The main difficulty of these problems is producing some unexpected and non-physical oscillation at material interface which causes entering some error in to computation domain. For eliminating this source of error, many sophisticated algorithm have been proposed recently. By neglecting diffusion processes, Euler equations and HLLC reimann solver are applied. In addition, Level set algorithm is implemented to track interferences between two materials. An accurate, easily developed and low computation cost algorithm, proposed by Abgrall and Karni, is used to prevent generating the oscillations in the interfaces. In the current work, the algorithm is developed to 2 dimensional algorithm. Afterwards, the result of 1 and 2 dimensional code are evaluated to verify the developed algorithm by some standard problems such as sod problem. Finally, shock –bubble (Air – Helium) interaction problem is simulated to investigate the effect of the algorithm in 2 dimensional simulation. The comparison shows that the code and its result have very good accuracy with very low computational cost.