Coalescence of grains was investigated using the two-sphere model to clarify the effects of boundary energy and grain size at the initial stage of sintering. The new rate equations for sintering and grain growth were derived by evaluating total surface energy and grain boundary energy of the system. The derivation was based on Inomata's free energy theory and Tanaka's definition of diffusion area and length for material transport. The rate equations included the ratio of the grain boundary energy to surface energy and the grain size ratio. Using the equations, coalescence of two spherical grains was simulated assuming that the sintering and grain growth phenomena take place simultaneously. The results showed that grain boundary expansion first occurs and then grain growth becomes dominant. It was also found that coalescence proceeds faster when the grain boundary energy is smaller.