The objective of this work was to investigate the influences of constitutive nonlinearities of brain tissue in numerical head model simulations by comparing the performance of a recently developed non-linear constitutive model with a simplified version, based on neo-Hookean elastic behaviour, and with a previously developed constitutive model. Numerical simulation results from an existing 3-D head model in the explicit Finite Element code MADYMO were compared. A head model containing a sliding interface between the brain and the skull was used and results were compared with the results obtained with a previously validated version possessing a tied skull-brain interface. For these head models, the effects of different constitutive models were systematically investigated for different loading directions and varying loading amplitudes in both translation and rotation. In the case of the simplified and fully non-linear version of the model of Hrapko et al., the response predicted with a head model for varying conditions (i.e. severity and type of loading) varies consistently with the constitutive behaviour. Consequently, when used in a finite element head model, the response can be scaled according to the constitutive model used. However, the differences found when using the non-linear model of Brands et al. were dependent on the loading conditions. Hence this model is less suitable for use in a numerical head model.