Rain induced instabilities are a common geotechnical problem especially in partially saturated soils. A large number of steep, natural or cut slopes remain stable for a long time and then fail during heavy rainstorms or after a long period of rain. In this work, the Material Point Method (MPM) is used to model the whole instability process. The MPM theoretical framework regarding a “single layer” of material points is extended to take into account interactions between solid gains and fluids within the pores (liquid and gas). A dynamic coupled hydro-mechanical formulation is considered hence the modelling of unsaturated soils is allowed. The paper presents the validation of the coupled formulation by means of an infiltration problem. Finally, the analysis of a theoretical slope failure induced by a heavy rain, which is inspired in real surface ruptures experienced by some embankment slopes is presented. A constitutive Mohr-Coulomb elastoplastic model is formulated in terms of net stress and suction in order to simulate the evolution of the material with the evolving suction.