We have developed a model for the flow of a thermosetting polymer at a constant flowrate through a straight cylindrical tube. Previous attempts at solving similar problems included a finite difference model on a fixed grid (tube geometry), and a finite element model on a moving grid (rectangular geometry). The first of these failed at large times because of the ever decreasing number of nodes in the central core. The second one was limited to the isothermal case, and was not checked against any experimental data. The present model improves the finite element/moving grid technique and applies it to the case of tube flow. Among the improvements incorporated are a better criterion to define when and how to move the grid, a non-uniform grid shrinkage technique that allows to follow more closely the shape of the buildup, a non-isothermal formulation, a mixed boundary condition that takes into account the insulating properties of the growing gel buildup and a rigorous dimensional analysis that leads to the proper consideration of the radial velocity component. The importance of all these points have been illustrated, and the model applied to available experimental data (Lipshitz, 1976; Castro et al., 1982). However, it fails for the case of very high flow rates.