The pressure applied during the sintering process plays an important role in improving the final density of UN pellets. In this work, a phase field model of UN pressure-assisted sintering was established by introducing elastic strain energy and particle rigid motion process. The effects of stress on the growth of sintering neck and rigid-body motion on the pore shrinkage were analyzed, and the multi-particle sintering process under the three mechanisms was simulated. The simulation results show that the length of the sintering neck and its growth rate increase with the increase in the applied strain. There is obvious stress concentration at both ends of the sintering neck, and the stress distribution gradually becomes uniform with the increase in time. With the increase in translational mobility, the pore shrinkage rate increases, and the densification completion time is advanced, while the value of rotational mobility has little effect on the pore shrinkage process. The model can capture the formation and growth of the sintering neck, the spheroidization and closure of the pores. The coordination grain number of large volume pores is higher and the existence time is longer.