The generation of multimodal virtual environments for surgical training is complicated by the necessity to develop heterogeneous simulation scenarios such as surgical incision, cauterization, bleeding, and smoke generation involving the interaction of surgical tools with soft biological tissues in real time. While several techniques ranging from rapid but nonphysical geometry-based procedures to complex but computationally inefficient finite element analysis schemes have been proposed, none is uniquely suited to solve the digital surgery problem. In this paper we discuss the challenges facing the field of realistic surgery simulation and present a novel point-associated finite field (PAFF) approach, developed specifically to cope with these challenges. Based upon the equations of motion dictated by physics, this technique is independent of the state of matter, geometry and material properties and permits different levels of detail. We propose several specializations of this scheme for various operational complexities. The accuracy and efficiency of this technique is compared with solutions using traditional finite element methods and simulation results are reported on segmented models obtained from the Visible Human Project.