This research is motivated by the need to design a Nuclear Magnetic Resonance Image guided surgical robot. The achievement of this objective requires the solution of two problems: design and construction of a magnetic resonance compatible mechanical manipulator and development of the appropriate robot control system. It is beneficial to keep robot actuators outside the magnet. Therefore, the parallel architecture should be used for the mechanical manipulator. Newly developed University of Western Australia Robot satisfies this requirement. Moreover, it has substantially larger workspace and torsional stiffness when compared to existing parallel configurations such as the Delta. The plausible method of dealing with the delays in the robot control system caused by the image analysis is the prediction of the deformation based on the mathematical model of the organ mechanical and geometric properties. The hyper-viscoelastic constitutive models offer a good way of representing non-linear stress-strain and stress-strain rate relations of soft tissues such as the brain. The numerical values for material constants for brain tissue are given. Additional advantage of the proposed model is that it can be easily implemented in commercially available finite element codes and immediately applied to large-scale computer simulations.