© 2019, OWZ. An improved version of the solid–liquid coupled material point method (MPM) is proposed to simulate ground collapses with fluidization involving transition processes from soil structures to flowing mixture. A water-saturated soil is assumed based on porous media theory, and the physical quantities of the soil and water phases are assigned to two separate sets of particles (material points). The main contribution of this study is the introduction of the fractional step projection method for the time discretization of the momentum equation of the water phase on the assumption of incompressibility. Thanks to this, the proposed solid–liquid coupled MPM is capable of suppressing the pressure oscillations caused by the weak incompressibility of water, which is commonly assumed in the previous studies, and of representing the wide range of behavior of the soil–water mixture at relatively low computational cost. Also, B-spline basis functions are utilized for the spatial discretization to suppress the cell-crossing errors caused by particles crossing element (cell) boundaries. Several numerical tests are conducted to examine the performance of the proposed method that inherits the beneficial features of MPM and demonstrate the capability of reproducing a model experiment of wave collision to sandpile that exhibits the water flow-induced fluidization process of soil involving scouring, transportation and sedimentation.