The aim of this paper is to analyse the influence of the polymer viscosity on the flow during the injection moulding process. A new method has been developed in order to easily represent a viscosity law exhibiting a Newtonian plateau at low shear rates, and a power-law dependence at high shear rates. In particular, the Cross law can be used without involving a dramatic increase of the computational cost through multiple quadratures in the gapwise direction during pressure calculations. Several examples are analysed and discussed.