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Gas metal arc (GMA) fillet welding is one of the most important processes for metal joining because of its high productivity and amiability to automation. This welding process is characterized by the complicated V-shaped joint geometry, a deformable weld pool surface, and the additions of hot metal droplets. In the present work, a three-dimensional numerical heat transfer and fluid flow model was developed to examine the temperature profiles, velocity fields, weld pool shape and size, and the nature of the solidified weld bead geometry during GMA fillet welding. The model solved the equations of conservation of mass, momentum, and energy using a boundary fitted curvilinear coordinate system. Apart from the direct transport of heat from the welding arc, additional heat from the metal droplets was modeled considering a volumetric heat source. The deformation of the weld pool surface was calculated by minimizing the total surface energy. Part I of this article is focused on the details of the numerical model such as coordinate transformation and calculation of volumetric heat source and free surface profile. An application of the model to GMA fillet welding of mild steel is described in an accompanying article (W. Zhang, C.-H. Kim and T. DebRoy, J. Appl Phys. 95, 5220 (2004)). © 2004 American Institute of Physics.