We tried to predict the parison shape in blow molding by non-isothermal viscoelastic flow simulation of a steady-state annular extrudate swell. The Phan-Thien Tanner (PTT) and the Carreau models including non-isothemal influence, were employed as the constitutive equation of viscoelastic and purely non-Newtonian fluid, respectively. Focused fluid was blow molding grade HDPE melt. Shape of extrudate swells greatly in the ratial direction because contraction flow is included in flow geometry of die. When an air flows around a parison, the temperature on the parison outer surface become decreased, but parison shape is almost independent of parison temperature at more than melting temperature.