The results of numerical simulation of laser drilling of aluminum, copper and steel samples using femtosecond and nanosecond pulses are presented. The drilling rates were predicted for a wide range of laser beam irradiance. The theoretical model utilized for the simulation was upgraded to include phase transition at the critical temperature. In the new theoretical approach the latent heat of evaporation was assumed to be temperature dependent, such that in the range below the critical temperature its value is practically constant, decreases rapidly as the temperature approaches the critical temperature and is zero at the temperatures exceeding the critical temperature. The computed drilling rates for 4 ns and 200 fs laser pulses are in agreement with the experimental data. The upgraded model provides explanation to the observed saturation of drilling rate dependence on laser pulse energy. A new method of determining critical temperatures of metals and metallic alloys is proposed.