Abstract: In this study, the 2D shallow water equations (SWE) are solved using a meshless method with the local polynomial approximation and the weighted-least-squares (WLS) approach. Three challenging dam-break flow problems are chosen to test the 2D meshless SWE model. The focus of this study is on the capability of simulating the shallow water flows with moving wet/dry fronts and large bottom slopes. Mass conservation, which is a very important concern in the wet/dry front problems, is carefully examined. Modification of the previous work on improving mass conservation is presented in this study. Computed results are compared with experimental data. The results show that the refined model can effectively simulate the flooding and drying with steep slopes in the topography.