Solidification processes play an important role in several industrial processes, such as weldingand additive manufacturing, and the resulting residual stress state is often critical for thestructural integrity of the material. A thermomechanical model was developed for the analysisand prediction of such solidification processes. The approach is based on a model proposed byRubin (Int. J. Eng. Sci. 25, 1175-1191, 1987). This plasticity model was formulated for finitestrains using an Eulerian evolution equation for a unimodular elastic distortional deformationtensor. This evolution equation automatically ensures thermodynamic consistency andpreservation of isochoric inelastic deformations. A 2D problem in the form of a butt weld jointwas analyzed. The main outcome from the analyses were the residual stress distributions. Theresults are compared to experimental data from the literature.