In this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times, tau(b) and tau(s). This asymptotic solution is found to be accurate up to strains of order unity and the branching priority, q, only affects the stress response at larger strains. The Pompom parameters fitted to extensional data are compared to LAOS data for three materials; two lightly branched metallocene catalyzed high density polyethylenes and a densely branched low density polyethylenes. In general, the Pompom model performs well in LAOS but tends to over predict experimental results at high strain amplitudes. (C) 2014 The Society of Rheology.