When non-spherical particles, like rods or discs, are added to a liquid the increase in viscosity of the mixture is often described by the Lipscomb model. One important result of Lipscomb’s model is that it predicts a strong increase in the viscosity of the suspension with increasing aspect ratio of the filler particles. Despite the fact that this model was originally proposed for a Newtonian matrix fluid it is also applied to polymer melts filled with non-spherical particles. Such an approach completely decouples the influence of the particle shape from the non-linear properties of the suspending fluid. Yet, since polymer melts often exhibit strong non-Newtonian behaviour, e.g. shear thinning, it is to be expected that such a superposition will give a wrong prediction of the suspension viscosity. To investigate this problem we performed a numerical study of a suspension based on a non-Newtonian matrix fluid and rigid spheroidal particles. In particular, we simulated an elongational flow of a Bird-Carreau fluid around spheroidal particles and used numerical homogenization to obtain the intrinsic viscosity of the suspension as function of applied rate of deformation, thinning exponent and aspect ratio. In the Newtonian regime we also compare with results from literature. In the transition region from Newtonian to non-Newtonian behaviour we obtained lower values of the intrinsic viscosity. In the power-law regime of the Bird-Carreau model, i.e. at high deformation rates, we found that the intrinsic viscosity of the suspension is independent of the applied rate of deformation. Further we obtained from the simulations that the intrinsic viscosity at high deformation rates strongly depends not only on the aspect ratio of the particles but also one the thinning exponent in the Bird-Carreau model, implying that the superposition approach in fact leads to a wrong prediction of the suspension viscosity at high deformation rates.