As opposed to the widely used explicit material point method (MPM), an implicit material point method (IMPM) is presented and investigated in this paper in the context of soil mechanics. A brief introduction to the IMPM formulation is described first, followed by two verification examples. It is found that energy conservation errors can be reduced greatly by choosing an appropriate time step size, although the method itself is unconditionally stable. A method of modelling the interaction between the soil and rigid bodies by fixing boundary velocities is detailed. Moreover, an elasto-perfectly plastic von Mises model is implemented into the IMPM framework, with the objective of gaining some preliminary understanding of the mechanism of progressive failure. A soil slope, on a foundation layer, subjected to two different loading conditions is investigated, for which two different failure patterns could be observed. For case 1, increased load is applied on the slope crest so that two distinct shear bands are formed as time progresses, showing that the evolution of failure may occur as a time-dependent progressive process; For case 2, gravity loading is initially applied and kept constant during the whole simulation, while the soil strength is reduced continuously. It is found that the slope collapses suddenly along a single failure surface. The results indicate that for simulating progressive failure modes, the IMPM has advantages that the computer model can continue to run and does not suffer from the mesh tangling as observed in the Finite Element Method.