Finite-element calculations are performed for the transient material and energy flow in a system to evaporate pure titanium. A 60-kW electron beam is used to heat the end of a 10.16-cm-diameter cylindrical rod, which is fed vertically through a water-cooled crucible. Vapor emanates from a liquid pool in which flow is driven strongly by buoyancy and capillary forces. At high evaporation rates, the vapor exerts strong shear and normal forces on the liquid-vapor interface. The MELT finite-element code is used to calculate transient, axisymmetric flow and temperature fields, along with liquid-solid and liquid-vapor interface locations. The influence of the vapor on the liquid top surface is treated using boundary conditions with parameters determined from Monte Carlo results. The upper and lower interfaces of the liquid pool are tracked using a mesh structured with rotating spines. The finite-element results show a characteristic response time of 20 ms to variations in electron beam power.