A hybrid Cellular Automata-Monte Carlo (CA-MC) approach is developed to simulate the sintering of particulate materials. The approach embodies a new, and physically realistic, way of simulating densification by grain boundary diffusion and collapse that takes into account the stresses arising from interactions with neighbouring particles (grains) by minimising the stored energy and energy dissipation rate using the variational principle. The parameters in the CA-MC simulations are calibrated in terms of measurable physical quantities by simulating the sintering of two identical contacting spheres, for which analytical solutions are well known and widely accepted. The use of the model is illustrated by simulating the densification of a randomly packed assembly of spherical particles. This demonstrates that the interactions between particles significantly inhibits shrinkage compared with that of two isolated spheres.