The simulation of erodible dambreak using two-layer shallow water equations and SNCHR scheme are elaborated in this paper. The results show that the two-layer SWE model in a good agreement with the data experiment which is performed by Louvain-la-Neuve Universit´e Catholique de Louvain. Moreover, the parallel algorithm with multicore architecture are given in the results. The results show that Computer I with processor Intel(R) Core(TM) i5-2500 CPU Quad-Core has the best performance to accelerate the computational time. Moreover, Computer III with processor AMD A6-5200 APU Quad-Core is observed has higher speedup and efficiency. The speedup and efficiency of Computer III with number of grids 3200 are 3.716050530 times and 92.9% respectively.