A Monte Carlo methodology different from others based on the Potts model has been developed to solve capillary-driven mass transport involved in the sintering process. The addition of a cohesive energy term to the energetic model enables quantification of the stress gradients within grains, as well as the induced mass fluxes. The study of two-particle sintering involving volume diffusion has been chosen as a first example. The morphological evolution of the two-particle system to a single particle is followed. Real-time-dependent neck growth and shrinkage rates are defined. The rheological behavior of the particles induced by the Monte Carlo procedure is discussed.