The CEA and the COGEMA, as part of their effort to model the different stages of the MOX fuel fabrication process, have specifically worked, on the sintering stage. A physical mechanistic model of MOX fuel sintering is proposed, as well as the numerical schemes that will lead to the achievement of the corresponding software tool. The model takes into account surface diffusion, grain boundary diffusion, volume diffusion, exchanges between solid and gas, as well as the mechanical strains of grains. The scale at which concentrations and strains are taken into account is smaller than grain size (0.1 mum for green pellets and 10 mum for sintered ones). The numerical resolution schemes of this problem have been conceived, and are also presented. They mainly consist of relaxation procedures to uncouple partial derivative mass conservation equations, flux balances along interfaces, non-linear potential equality conditions at interfaces, and Navier-Lame equations over each grain. A code (SALAMMBO) is under construction, based on the latter; once validated by experimental and parametric tests, this code will describe Pu distribution, grain and pore size distribution, and local density of the pellets as functions of the sintering conditions, thus enabling further developments of the fabrication process such as the obtention of advanced microstructures of improved MOX fuels.