Abstract: The heat dissipation of anodes or collectors is one of the essential problems in the design of high power electron device. In recent twenty years high efficient vaporization cooling structure has been developed, but its design is still done by means of simulation or empirically. In this paper, a mathematical model for the vaporization cooling eleetrode and its solving method are provided. The nonlinear and multi-valued proporties of this mathematical physical equation are discussed. As an example, a numerical solution of inner temperature field in a typical vaporization cooling electrode, an anode of high power electron tube has been given with digital computer. On the basis of these results, the design of vaporization cooling electrode and estimation of its heat dissipation capability are possible.