Hybrid welding combines laser and arc welding to overcome their individual short comings. While much of the current literature has focused on experimentally demonstrating the benefits of hybrid welding, work on the quantitative understanding of the governing physical processes is just beginning. In this work, a three dimensional steady numerical model for solving the equations of conservation of mass, momentum, and energy is developed and tested to understand the temperature fields, cooling rates, and fusion zone geometry for hybrid welding. The results show that hybrid welding increases weld pool width, which can lead to improved gap bridgability relative to laser welding alone. Increasing laser power leads to a deeper and wider hybrid weld pool. When the arc and laser are in close proximity, calculations showed that arc radius must decrease to achieve the observed weld depth.