Experimental shear and tensile stress growth coefficients for startup of steady shear and uniaxial elongation for a commercial grade acrylonitrile-butadiene-styrene (ABS) polymer melt are presented. One differential [Phan-Thien and Tanner (PTT)] and two Kaye-Bernstein-Kearsley-Zapas (K-BKZ) type single integral [Wagner and Papanastasiou-Scriven-Macosko (PSM)] nonlinear viscoelastic constitutive models were fit to shear and extensional experimental data. A comparison of the fit quality was performed, and the PTT model was found to result in the best overall quality fit, although deviations from linear viscoelastic behavior at small extensional strains could not be adequately described by the linear viscoelasticity theory without a time correction. Experimental data for stress relaxation after cessation of both steady shear and uniaxial elongation were compared with three constitutive model predictions in order to evaluate their anticipated accuracy in the prediction of residual stresses. The PTT model provided better predictions of ABS relaxational behavior than K-BKZ models except for shear stress relaxation in the nonlinear regime. Qualitative differences between experimental data and model predictions were found to be present for all models tested at large shear and extensional strains.