The non-linear mechanical behaviour of porcine brain tissue in different deformation modes is de- termined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory experiments, stress relaxation experiments and constant strain rate experiments are presented. Large deformations at the time scale of loading and the material behaviour during complex loading paths (loading-unloading) is investigated. No significant immediate mechanical damage is observed for these shear deformations. A new differential viscoelastic model is used to describe the non-linear mechanical response of brain tissue. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.