Abstract: The electric field distribution of the dielectric surface was computed by a numerical simulation method. The physical mechanism of influencing dielectric surface flashove was analyzed. Four models of the radically dielectric structures were given and the comparison of the electric field strengths at the triple compination point and dielectric surface among the four kinds of structured was made. In addition the effects of an applied guide magnetic field, the emission of electrons and return electron flow on the surface flashover were also considered. Some istructive results for designing the dielectric structures with optimized parameters were obtained.