In this paper, the SPH method is applied to evaluate stability of a slope and to simulate the gross discontinuities after failure. Herein, the Drucker-Prager model with non-associated plastic flow rule is employed to describe the elasto-plastic soil behaviour. The shear strength reduction method is applied to estimate the safety factor of a slope, while critical slip surface is automatically determined from contour plot of accumulated plastic strain. To take into account the pore-water pressure, a new SPH momentum equation is proposed. It is shown that by using this new expression of momentum equation, the free-surface boundary condition between water and submerged soil is automatically imposed without explicitly implementing a computational procedure to calculate an external force (pressure force). This paper suggests that the new SPH momentum equation developed herein is also applicable for further developments of SPH for saturated/unsaturated soils. As an application of the proposed method, slope stability analyses and slope failure simulations of a two-side earth embankment are performed and then comparing with traditional solutions. Very good agreements with limit equilibrium method and finite element method (FEM) have been obtained. This suggests that SPH is a promising method for the current application, especially for handling large deformation and failure of a slope subjected to heavy rainfall or earthquake loading.