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A quantitative model for liquid phase sintering is developed based on the following ideas. During heating a liquid phase forms, which is easily mobile, wets the solid particles completely, dissolves solid atoms and provides an easy diffusion path for them. The solid density increases by particle rearrangement and by the flattening of particle contacts. Driving (or retarding) forces result from capillary stresses, from applied mechanical stresses, from the pressure of gas entrapped in closed pores and from differences in chemical potential of the dissolved and precipitated matter. At higher densities the driving force may become very small, since the liquid pressure decreases and a negative contribution from the solid-liquid interface energy increases. At this stage grain coarsening plays an important role for the continued filling of larger and larger pores. The model is applied to describe nonisothermal densification curves measured on Si 3 N 4 for various hold temperatures, axial stresses and green densities. Adjusting a moderate number of parameters all having a physical meaning leads to good agreement between theory and experiment.