A coupled Cellular Automaton (CA) - Finite Element (FE) model is proposed to predict the grain structure formation during Gas Tungsten Arc Welding (GTAW). The FE model solves the heat flow problem based on an adaptive meshing. This is done on a first FE mesh. The CA model simulates the development of the envelope of the grains in the liquid. For that purpose, a second FE mesh, referred to as CA mesh, is used. Fields can be interpolated between the adaptive FE mesh and the CA mesh. A CA grid made of a regular lattice of cubic cells is defined and superimposed onto the CA mesh. A new dynamic strategy for the allocation/deallocation of the CA grid is proposed to reduce the computation and memory costs. This CAFE model is applied to partial melting of an initial grain structure and epitaxial growth in the undercooled zone of a liquid pool, thus simulating the formation of solidification structure during the GTAW process. Examples of single linear passes simulations for various processing conditions and a multiple pass simulation are presented.