Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.