Soft particle materials such as some pharmaceutical and food products are composed of particles that can undergo large deformations under low confining pressures without rupture. The rheological and textural properties of these materials are thus governed by both particle rearrangements and particle shape changes. For the simulation of soft particle materials, we present a numerical technique based on the material point method, allowing for large elasto-plastic particle deformations. Coupling the latter with the contact dynamics method makes it possible to deal with contact interactions between particles. We investigate the compaction of assemblies of elastic and plastic particles. For plastic deformations, it is observed that the applied stress needed to achieve high packing fraction is lower when plastic hardening is small. Moreover, predictive models, relating stress and packing fraction, are proposed for the compaction of elastic and plastic particles. These models fit well our simulation results. Furthermore, it is found that the evolution of the coordination number follows a power law as a function of the packing fraction beyond jamming point of hard particle packings.