Three dimensional solution for the heat flow in laser beam welding with a constant moving Gaussian heat source has been analyzed. The temperature rise and cooling rate are related to the beam spot size, travel speed and laser power. As an application of this model, the theoretical predictions were compared to the experimental data in which laser conditions were arranged for carbon and AISI 316 steels as bead-on-plate welds, using a continous wave 3kW CO2 laser with the various travel speed, beam sport size and laser power. Experimental data show a good agreement with the theoretical predictions. This analytical model can be used to determine the maximum possible penetration depth, fusion boundary, and thermal history for given sources of laser beam welding conditions.