Butt-fusion welding process is used to join the polymeric pipes. Recently, some researchers suggest the curved surface to enhance a welding quality. We investigated how curved welding surface affects heat and flow behaviors of polymer melt during the process in 2D axisymmetric domain with finite element method, and discussed the effect to the welding quality. In this study, we considered HDPE pipes. In heat soak stage, curved phase interface between the melt and solid is shown along the shape of welding surface. In jointing stage, squeezing flow is generated between curved welding surface and phase interface. The low shear rate in fusion domain reduces the alignment of polymer to the perpendicular direction of pipes, and then this phenomenon is expected to help to enhance the welding quality.