The incident energy flux impinged on the free surface of liquid layer was considered to be balanced with the latent heat in evaporation and the heat in directional conduction but neglecting convective heat transfer due to a small Peclet number at the cavity base. The quasi-steady state model was developed in this study to analyze the effect of the energy density during the penetration process and an exponential expression for penetration velocity as a function of liquid-thickness and temperature was also derived. The penetration velocity versus energy density calculated by the present model showed good agreements with the experimental data for drilling copper, which the relative errors between the calculated and the experimental data are less than 15%. By the setup of non-uniform grids distribution in numerical method, this work had successfully predicted the variation of the penetration velocity with energy density distribution. The effects of the energy density on flow rate, thickness of liquid layer, base temperature of fusion zone had also been discussed in this study.