This work presents a two-dimensional quasi-steady state model to study the fluid flow and heat transfer in high-power density welding process of thin AISI-304 stainless steel plates. The enthalpy method and the finite volume method were used for a numerical analysis of the mushy region phase change as well as the heat flow at the weld pool and the heat-affected zone. The results show that the mushy region distributed around the weld pool becomes wider downstream and the surface heat losses by convection and radiation can be significant factors in welding process especially when a welding speed is relatively low.