Traditional medical education has relied on training with real patients in actual clinical setting under the supervision of an experienced surgeon. Novice surgeons can make mistakes that result in risks to patient safety. Computer simulation-based training has been proposed to complement traditional training to improve patient safety and surgeon efficiency and reduce cost and time. Surgical simulation allows surgeons to learn, practice and repeat surgical procedures to gain experience in a realistic and safe environment. This dissertation focuses on the development of computer-based surgical simulations. Physically based modeling is used to model deformable objects to mimic human organs in simulation. Such a simulation is composed of many simulation objects whose behaviors are represented by differential equations. The system of differential equations can be solved by using numerical integration algorithms. Moreover, physical intersections between the objects require the computation of collision detection and response between objects. This dissertation studies the determination of elasticity parameters in lumped element models, the trade-offs in numerical integration algorithms for finding the suitable numerical integration algorithms and time step size of simulation objects, and the collision detection and response algorithms for deformable objects. Improvements and extensions of the open source/open architecture GiPSi surgical simulation framework are also presented. An endoscopic third ventriculostomy simulator is constructed using the GiPSi framework as a test bed of the specific tools and methods developed.