Material point method (MPM) offers an effective approach for analysing large-deformation problems, such as landslides that often involve unsaturated soil. Several MPM formulations for unsaturated soil have been reported in the literature, but they assumed that water retention ability and permeability function are independent of soil deformation. Furthermore, most studies used a single set of material points, so they cannot simulate some processes (e.g., the infiltration of free water into unsaturated soil). To address these problems, a two-point MPM formulation has been extended from saturated to unsaturated soils, considering the influence of porosity change on the water retention curve and permeability function. The information of solid and liquid phases is carried by two individual sets of material points, assuming zero air pressure. The elastoplastic mechanical behaviour is modelled by the Drucker-Prager model using Bishop's stress. The MPM simulations were compared with the results of physical model tests (for large-deformation problems) and finite element analysis (for smalldeformation problems). It is evident that the proposed MPM formulation is able to capture various hydromechanical problems well. In particular, the computed failure processes of unsaturated soil slope under rainfall are consistent with results from physical model tests.