The addition of rod-like filler particles to a liquid leads to a noticeable increase in the viscosity of the mixture. The effect can be described by the Dinh and Armstrong model [1]. One important result of this model is the prediction of a strong increase in the viscosity of the suspension with increasing aspect ratio of the rigid rods. Despite the fact that this model was originally proposed for a Newtonian matrix fluid it is also applied to polymer melts filled with rod-like particles. Such an approach completely decouples the influence of the rod aspect ratio 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 consisting of a non-Newtonian matrix fluid and rigid rods. In particular, we simulated different flows of a Carreau fluid around rigid rods with different orientations and used numerical homogenization to obtain the intrinsic viscosity of the suspension as function of applied rate of deformation, thinning exponent and aspect ratio of the rod. In the power law regime of the Carreau model we compare our numerical results with analytical models of Souloumiac and Vincent [2] and Gibson and Toll [3]. [1] S. M. Dinh and R. C. Armstrong. Journal of Rheology 28.3 (1984), pp. 207–227. [2] B. Souloumiac and M. Vincent. Rheologica Acta 37.3 (1998), pp. 289–298. [3] A. G. Gibson and S. Toll. Journal of Non-Newtonian Fluid Mechanics 82.1 (1999), pp. 1–24.