Surgical simulation of soft tissues is an increasingly viable tool for predicting surgical outcomes and in training medics and residents. Simulated procedures include laproscopic surgery, craniofacial reconstruction, z-plasty, breast reduction, gastrointestinal surgery and reconfiguration of musculoskeletal geometry. In these and many other scenarios, a subject specific simulation environment in which procedures can be practiced is of immeasurable value for training as well as for actual research and development of surgical techniques. Several technological and algorithmic problems currently limit the applicability of surgical simulation; the solutions to these problems require collaboration between mathematicians, computer scientists, engineers and clinicians. For example, until recently most simulation techniques for soft tissues were too computationally burdensome to be applicable in a real or interactive time environment. Offline computations have always been of use in helping to determine the results of a procedure, however many algorithms were developed that sacrificed accuracy for speed in an attempt to satisfy interactive frame rates. In the process, many of these algorithms were doomed to produce scientifically unreliable results making them of little use in accurately predicting surgical outcomes. As computer performance improves, computational power is less and less frequently precluding the use of more widely accepted scientific computing algorithms for soft tissues at interactive rates. Also, larger regions of the body can be simulated (e.g. in examining musculoskeletal procedures related to motion). In this short course, we will be investigating the most promising directions for algorithm design, use of architectures, surgical simulation interface design and procedures that lend themselves to simulation by encouraging interdisciplinary cooperation between medicine, engineering, applied math and computer science.