The computer modelling of soft tissue has applications in the simulation of surgical procedures, product design, and in CAD generally as well as in motion pictures. We begin by reviewing computer modelling techniques in a range of applications. Algorithms are described to predict where surfaces interact mechanically, aiming as far as possible to use geometric modelling methods available within high level CAD systems. After an initial 2-Dimensional evaluation, 3-dimensional surfaces were used throughout. A model was developed to predict the region of impact of two surfaces in an environment of many surface patches. We report the results of this modelling and the application of refinement algorithms to reduce the computation requirements. We then go on to discuss the applicability of this work in the modelling of the deformation behaviour of soft tissues.