Soft granular materials are composed of grains can deform elastically or plastically without rupture under low confining pressure. They occur in numerous applications in chemical, pharmaceutical, cosmetic and food products. Joint effects of disorder and large grain deformations lead to novel mechanical properties that differ from those of hard granular materials. Indeed, a combination of grain rearrangements and grain shape change controls the rheological and textural properties of soft granular materials. In this work, we investigate the compaction of assemblies of elastic and plastic grains using an original numerical approach. It is based on coupling of the Material Point Method allowing accounting different mechanical behaviours (elastic, plastic…) of individual grains, and the Contact Dynamics method for dealing with contact interactions between grains [1-3]. In this study, compressibility rates ranging from fully compressible to incompressible grains are considered for elastic grains. We show that the uniaxial stress declines as the grain compressibility decreases, and the packing can deform considerably. For the plastic grains, it is observed that one needs less applied stress to achieve high packing fraction when the plastic hardening is small. Moreover, the predictive models, relating the applied stress to the packing fraction, are proposed for the compaction of elastic and plastic grains. These models fit well the simulation results. Furthermore, for both cases, the evolution of the coordination number is related to the packing fraction by a power-law function beyond jamming transition.References.[1] S. Nezamabadi, F. Radjai, J. Averseng, J.-Y. Delenne, “Implicit frictional-contact model for soft grain systems”, Journal of the Mechanics and Physics of Solids, 83: 72-87, 2015.[2] S. Nezamabadi, T.-H. Nguyen, J.-Y. Delenne, F. Radjai, “Modeling soft granular materials”, Granular Matter, 19: 8, 2017.[3] S. Nezamabadi, X. Frank, J.-Y. Delenne, J. Averseng, F. Radjai, “Parallel implicit contact algorithm for soft grain systems”, Computer Physics Communications, 237: 17-25, 2019.