Brain tissue accommodates non-linear deformations and exhibits time-dependent mechanical behaviour. The latter is one of the most pronounced features of brain tissue, manifesting itself primarily through viscoelastic effects such as stress relaxation. To investigate its viscoelastic behaviour, we performed ramp-and-hold relaxation tests in torsion on freshly slaughtered cylindrical ovine brain samples (25 mm diameter and ∼10 mm height). The tests were conducted using a commercial rheometer at varying twist rates of {40, 240, 400} rad m s, with the twist remaining fixed at ∼88 rad m, which generated two independent datasets for torque and normal force. The complete set of viscoelastic material parameters was estimated a simultaneous fit to the analytical expressions for the torque and normal force predicted by the modified quasi-linear viscoelastic model. The model's predictions were further validated through finite element simulations in FEniCS. Our results show that the modified quasi-linear viscoelastic model-recently reappraised and largely unexploited-accurately fits the experimental data. Moreover, the estimated material parameters are in line with those obtained in previous studies on brain samples under torsion. These material parameters could enhance our understanding of slow-progressing pathologies such as tumour growth or neurodegeneration and inform the development of improved models for brain surgery planning and training. Our novel testing protocol also offers an efficient, robust and reliable method for determining the viscoelastic properties of brain tissue under much more rapid loading conditions, which are of crucial importance for modelling traumatic brain injury.