A three-dimensional axis-symmetry model of the fluid flow and heat transfer of laser melted pool is developed. The model corresponds physically to a stationary laser source. Non-dimensional forms of the governing equations are derived. Four dimensionless parameters arise from the non-dimensionalization, namely, Marangoni number, Prandtl number, Dimensionless melting temperature, and Radiation factor. Their effects and significances are discussed. Numerical solutions are obtained. The solid liquid interface, which is not known a priori, is solved. Quantitative effects of the dimensionless parameters on pool shape are obtained. In the presence of the flow field, the heat transfer becomes convection dominated. Its effect on isotherms within the molten pool is discussed. Experimental results are presented.