The article deals with the effect of the first and the second normal stress difference on the predicted flow front and pressure distribution during the filling stage of the thermoplastic injection molding. The normal stresses are predicted using the non-linear Criminale-Ericksen-Filbey model incorporated into a comprehensive 3D simulation software for moldfilling analysis. The model parameters are estimated from the viscosity curves using the Abnormal Cox-Mertz rule. The additional term improves the prediction of the so called ear-flow effect (melt racing on the edge of the cavity) as well as pressure predictions at high injection rates.