Soft-particle materials include colloidal pastes, vesicles, many powders, microgels and suspensions. They share the common feature of being composed of particles that can undergo large deformations without rupture. For the simulation of such materials, we present a modelling approach based on an implicit formulation of the Material Point Method (MPM) interfaced with the Contact Dynamics (CD) method for the treatment of frictional contacts between particles. Each particle is discretized as a collection of material points. The information carried by the material points is projected onto a background mesh, where equations of motion are solved. The mesh solution is then used to update the material points. The implicit formulation of MPM allows for unconditional numerical stability and efficient coupling with implicit treatment of unilateral contacts and friction between the particles by the CD method. We use this model to analyse the compaction process of 2D soft-particle packings. The packing can reach high solid fractions by particle shape change and still flow plastically. The compaction is a nonlinear process in which new contacts are formed between particles and the contact areas increase. We find that the evolution of the packing fraction is a slow logarithmic function of the driving stress as a consequence of increasing contact area. We also evidence the effect of friction, which favours strong stress chains and thus the elongation of particles, leading to a larger packing fraction at a given level of compressive stress as compared to a frictionless particle packing.