Real-time surgical simulation often requires computing the deformations of visco-elastic human-body tissue and generating both graphic and haptic renderings. As human users are more sensitive to small haptic discrepancies than visual ones, good force rendering requires a refresh rate of 500 Hz or more, which is far beyond the capabilities of current simulators. Moreover, if the simulator runs on a remote server, limited bandwidth, network latency and variance further compromise the quality of haptic rendering. To address these problems, a new interpolation-extrapolation data structure called the forcegrid is proposed, which makes it possible to approximate forces at rates greater than 500 Hz, regardless of the complexity of the simulated object. The forcegrid is designed for haptic interaction with continuous contact. It is a regular grid defined over the virtual workspace, in which every vertex contains a force. An extrapolation algorithm updates this force at every simulation cycle, while an interpolation algorithm computes the force to be rendered on the haptic device at the desired rate. The forcegrid has been successfully tested on various virtual deformable objects.