ABSTRACT In this Ph.D. thesis a new deformable model (ParSys) has been presented. Like other deformable models, ParSys allow the incorporation of elasticity to the 3D geometric models. ParSys is based on linked volumes. In this model the speed is the most important characteristic over the precision although it has a realistic behaviour because it uses real physical parameters. PasSys has the following main features: * ParSys is quick to calculate, almost as fast as the simplest deformable heuristic models based on mass-spring. * ParSys allows topological changes easily (like incisions). * The parameters that govern the deformation can be based on real physical parameters (Young modulus), like the models based on continuous mechanics. * ParSys has a volumetric behavior, which allows a greater visual realism. * ParSys does not need to know the objects internal structure to obtain the particle system that controls the deformation. The experimental results in this thesis prove that ParSys is an ideal model for their use in interactive virtual environments, like the surgical simulation.