Soft particle materials are composed of discrete particles that can undergo large deformations without rupture. Most food products, many powders, colloidal pastes, vesicles and biological cells are soft particle systems. In order to model such materials, we present an efficient numerical approach combining an implicit formulation of the Material Point Method (MPM) and Contact Dynamics (CD) method. The MPM deals with bulk variables of an individual particle by discretizing it as a collection of material points, whereas the CD allows for the treatment of frictional contacts between particles. This model is applied for the simulation of the uniaxial compression of 2D soft-particle packings. The compaction is a nonlinear process in which new contacts are formed between particles and the contact areas increase. The change of particle shapes allows these materials to reach high packing fraction. We find that the contact specific surface, the orientation anisotropy and the aspect ratio of particles increase as a function of the packing fraction but at different rates. We also evidence the effect of friction, which favors strong stress chains and thus the elongation of particles, leading to larger values of the orientation anisotropy and the aspect ratio at a given level of packing fraction as compared to a frictionless particle packing.