Before flashover across an insulator under high electric field in vacuum, there are charging phenomena occurring on the insulator surface, which significantly affect the developing process of flashover. Based on the secondary-electron-emission-avalanche model and by using the Monte Carlo method, a 2-D analysis of surface charge density on cylindrical and conical insulators prior to flashover in vacuum has been performed under unipolar voltage. Different materials are employed, i.e., alumina ceramic, PTFE, PMMA, and PI. The influences of materials, voltage amplitudes, and coning angles on charge distribution are investigated. The results reveal that negative charges exist in a small surface region near the cathode, while the surface charges positive in a larger region away from the cathode. With increasing applied voltage, both the negative charge density and region decrease, and even vanish, whereas both the positive charge density and region increase, and the peaks of both regions move toward the cathode. For the conical insulator with a negative angle, the positive charge density is greater than that with a positive angle, and the simulation describes well experimental data relating the coning angle, the surface charge, and the flashover voltage.