This paper presents a dynamic fully coupled formulation for saturated and unsaturated soils that undergo large deformations based on material point method. Governing equations are applied to porous material while considering it as a continuum in which the pores of the solid skeleton are filled with water and air. The accuracy of the developed method is tested with available experimental and numerical results. The developed method has been applied to investigate the failure and post-failure behaviour of rapid landslides in unsaturated slopes subjected to rainfall infiltration using two different bedrock geometries that lie below the top soil. The models show different failure and post-failure mechanisms depending on the bedrock geometry and highlight the negative effects of continuous rain infiltrations.