Coal mining waste dumps are representative artificial accumulations of bulky rock and soil material. Certain factors make these dumps possess characteristics such as selforganized criticality, nonlinear shear strength of the waste accumulation. We discusse the main waste dump characteristics and subsequently produced numerical simulations of the stability of waste dumps of various heights using the Fast Lagrangian Analysis of Continua and based on the HoekBrown nonlinear strength criterion. The simulation calculation results show that the stability is a dynamic evolving process corresponding to increasing waste dump height. Safety factors, based on a nonlinear rule, vary with the waste dump height. Theoretical analysis and calculated outcomes reveal a progressive failure rule of waste dumps, and all indicate the methods we put forward are reasonable.