The present paper has made it possible to highlight the thermo-mechanical behavior of the bead weld by the butt fusion welding process of two high-density polyethylene (HDPE) pipes. We proposed a welding technic for assembly two plastic pipes to see the effect of fluid pressure and the stress distribution during the welding process at the bead weld. To answer this objective, we wrote a finite element program named D-flux in Fortran95 language then we implemented the (For) files within the finite element code. The numerical simulation by Finite element makes it possible to evaluate the relevance of the proposed approach and validate the accepted hypotheses for this welding process. This numerical simulation of the thermal cycles of welding was conducted to evaluate the impact of welding on bead weld behavior.