In this paper the numerical scheme developed by Pan and Cocks (Acta metall. 43, 1395–1406, 1995) is used to simulate the co-sintering process of two spherical particles of different sizes by coupled grain-boundary and surface diffusion. The numerical analysis reveals many interesting features of the co-sintering process. For example, it is found that the shrinkage between the two particles is not affected significantly by the size difference of the two particles as long as the difference is less than 50%. Based on the numerical results, empirical formulae for the characteristic time of the co-sintering process and for the shrinkage rate between the two particles are established. The empirical formulae can be used to develop constitutive laws for early-stage sintering of powder compacts which take into account the effect of particle size distribution. To demonstrate this, a densification rate equation for compacts with bimodal particle size distributions is derived.