A finite element model has been developed for the 3D simulation of the sintering of a single track during a selective laser sintering process (SLS). The model takes into account both the thermal and the sintering phenomena involved in the process. Owing to the continuous movement of the laser beam the model takes also into account the transient nature of the problem. This is transformed into a pseudo‐static one through a transformation of the coordinates system of the equations. Nevertheless, this transformation introduces a convective term into the heat equations that produces instabilities in the solution. These instabilities have been solved by using a stream upwind Petrov Galerkin (SUPG) strategy together with a shock capturing scheme. Finally, a fixed point strategy is used for the solution of the analysis. The model has been tested through the solution of some examples.