Yes / An approximation to the Phan-Thien Tanner (PTT) constitutive model is developed with the aim of giving low-cost simulation of Gas Assisted Injection Moulding (GAIM) while incorporating important viscoelastic characteristics. It is shown that the developed model gives a response typical of full viscoelastic models in transient and steady state uniaxial and constant shear rate deformations. The model is incorporated into a 3D finite element GAIM simulation which uses the ‘pseudo-concentration’ method to predict residual polymer, and applied to published experimental results for a Boger fluid and a shear-thinning polystyrene melt. It is shown that the simulation gives a very good match to published results for the Boger fluid which show increasing Residual Wall Thickness (RWT) with increasing Deborah number. Against the shear-thinning polymer, the quality of match depends upon which of two ‘plausible’ relaxation times is chosen; qualitatively different results arise from two different means of estimating a single relaxation time. A ‘multi-mode’ approach is developed to avoid this uncertainty. It is shown that the multi-mode approach gives decreasing RWT with increasing Deborah number in agreement with the published experimental results, and avoids the issues that arise from estimating a single relaxation time for a molten polymer.