Abstract: For investigating the mechanism of high power microwave flashover and breakdown on dielectric surface, the theoretical modeling is put forward, including dynamic equations, particle-in-cell method, secondary emission and Monte-Carlo collision between electrons and gas atoms. Based on the theoretical model, the 1D3V PIC-MCC code is programmed. By using this code, we numerically study vacuum multipactor discharge, volume breakdown under high-pressure gas and surface breakdown under low-pressure gas course, including the number of electrons and ions, electron trajectories, electron and ion density distributions, the time and space distribution of space charge field, the average electron energy, the average energy of impact electrons, the number of impact electrons, electron energy distribution functions, average secondary emission ratio and energy balance. The numerical results are concluded as follows: vacuum multipactor could not cause breakdown for low deposited power (about 1% microwave power); volume breakdown is caused by high-level number of electrons with low energy, the breakdown position is far from dielectric surface, and the forming time is at the level of microseconds; flashover and breakdown on dielectric surface are caused by the continuous increase of deposited power resulting from many high-energy electrons, the breakdown position is near to dielectric surface, and the forming time is at the level of nanoseconds.