The technique of weaving by magnetic arc deflection was developed a few years ago to enable the oscillation of the weld pool, thus, causing grain refinement and improving the properties on the welded joint. This paper aims to propose two heat source models that include effects of magnetic arc deflection on a bead-on-plate GTAW process in numerical simulations by using the finite element method. Two cases are studied. In the first case, non-deflected arc and straigth magnectic deflected arc along the torch movement are carried out and compared to numerical simulations. Temperatures at three different points on the backside of the plates (two away from the welding center line and one in its center) and weld pools of SAE 1020 3.2 mm and 6 mm thick steel plates are analyzed. Results obtained by numerical simulations are close to the experimental ones. In the second case, welding with weaving (frequency of 1Hz) on 3 mm thick steel plates is analyzed. The bead width and its visual presentation are compared to experimental results, which show good agreement with both proposed models.