Energid is developing a realistic surgery simulator that delivers high fidelity visual and haptic feedback based on the physics of deformable objects. Modeling the interaction of surgical tools with soft biological tissue in real time poses challenges because the precise physical models of organs are not readily available, and the simulation of the behavior of tissue has a high computational burden. In this paper we present a realistic surgery simulation technique which inlcudes novel algorithms for simulating surgical palpation and cutting. We implement a meshfree numerical technique for realistic surgery palpation simulation. Simulation of surgical cutting is one of the most challenging tasks in the development of a surgery simulator. Changes in topology during simulation render precomputed data unusable. Moreover, the process is nonlinear and the underlying physics is complex. We propose a hybrid approach to the simulation of surgical cutting procedures by combining a node snapping technique with a physically based meshfree computational scheme.