Interactive surgical simulators capable of providing a realistic visual and haptic feedback to users are a promising technology for medical training and surgery planification. However, modelling the physical behaviour of human organs and tissues for surgery simulation remains a challenge. On the one hand, this is due to the difficulty to characterise the physical properties of biological soft tissues. On the other hand, the challenge still remains in the computation time requirements of real-time simulation required in interactive systems. Real-time surgical simulation and medical training must employ a sufficiently accurate and simple model of soft tissues in order to provide a realistic haptic and visual response. This study attempts to characterise the brain tissue at similar conditions to those that take place on surgical procedures. With this aim, porcine brain tissue is characterised, as a surrogate of human brain, on a rotational rheometer at low strain rates and large strains. In order to model the brain tissue with an adequate level of accuracy and simplicity, linear elastic, hyperelastic and quasi-linear viscoelastic models are defined. These models are simulated using the ABAQUS finite element platform and compared with the obtained experimental data. (C) 2015 Elsevier Ltd. All rights reserved.