In Laser Beam (L.B.) and Electron Beam (E.B.) drilling, the energy distribution significantly affects both the penetrating efficiency and working performance, both of which are usually estimated by numerical skill or experimental measure. Through the application of a stimulation model, an unstable solution with the finite difference method will result near the solidliquid interface unless much finer grid sizes are set up. To improve on the above defect, nonuniform grids are therefore utilized; this will complicate the built-up of the program and also easily causes the simulated energy distribution to be divergent in the iteration process. In this study, an estimated small Peclet number and observed narrow-deep cavity made the convective and radial diffusion terms small enough to be neglected in the governing equation. From these assumptions, the model was then used to investigate the drilling efficiency where two-phase flow convection could be simplified further into one dimension and thus the analytical solution becomes possible by transferring the penetration velocity into the logarithmic form. When compared with the experiment made by Allmen  , the present model shows good agreement in higher energy density and relative errors are no more than 10%.