A numerical method for inverse thermal analysis of steady-state energy deposition in plate structures is constructed according to the general physical characteristics of energy deposition within a volume of material from a beam energy source. This numerical method represents implementation of a general methodology using basis functions that was introduced previously. The formal structure of the numerical method presented follows from a specific definition of the inverse heat transfer problem, which is well posed for inverse analysis of heat deposition processes. This definition is based on the assumption of the availability of information concerning spatially distributed boundary and constraint values. This information would be obtained in principle from both experimental measurements obtained in the laboratory, as well as numerical simulations performed using models having been constructed using basic theory. Experimental measurements include solidification cross sections, thermocouple measurements, and microstructural changes.