A metal molten-pool is described by the Navier-Stokes and energy equations and the depressed liquid surface is described by the Young-Laplace equations,and the metal evaporation is described by the BGK equation. The velocity and temperature distributions of the pool and the vapor heated by an electron gun are solved by the finite difference method. The numerical results show the evaporation rate of the metal increases with the power of the electron gun, so the vapor density increases and the vapor temperature decreases and the vapor velocity increases. The surface temperature of the pool with the depressed surface is less than the one of the pool with the plane surface, so is the metal evaporation rate. The difference of the evaporation rate between them increases with the power of the electron gun, so the liquid surface depression should be taken into consideration for a high power electron gun.