In the polymer processing, weld-lines often occur and cause the degradation of the mechanical and optical properties of products. These properties are degraded when the polymer molecules near the weld-line highly orient owing to the elongational flow and the orientation is fixed by solidification of the polymer melts before it returns to a random condition. In the present paper, the viscoelastic welding flow was numerically calculated for analyzing the molecular orientation in the weld-line region. The numerical simulation of the flow around a spider supporting a mandrel was carried out using the single-mode Giesekus model as a constitutive equation. The effects of the spider shape and viscoelastic properties of polymer melts on the anisotropy of the molecular orientation at the weld-line were analyzed. The calculation was carried out for three spider shapes, i.e. the spider-rear-end-angle 9=300, 45°, and 60°. The numerical results showed a simple modification of 9 suppressed the elongational rate, the stress, and the maximum value of the degree of the molecular orientation near the spider rear end, where the weld-line occurred. When the Weissenberg number is large and the influence of shear-thinning is great, the maximum value of the elongational rate was sensitive to 9. Especially at large Weissenberg number (=2.4), the elongational stress was reduced more effectively using the spider of the case that O600.