Today, there is growing interest in computer surgical simulation to enhance surgeons' training. This paper presents a simulation system based on novel algorithms for animating instruments interacting with deformable tissue in real-time. The focus is on computing the deformation of a tissue subject to external forces, and detecting collisions among deformable and rigid objects. To achieve real-time performance, the algorithms take advantage of several characteristics of surgical training: (1) visual realism is more important than accurate, patient-specific simulation; (2) most tissue deformations are local; (3) human-body tissues are well damped; and (4) surgical instruments have relatively slow motions. Each key algorithm is described in detail and quantitative performance-evaluation results are given. The specific application considered in this paper is microsurgery, in which the user repairs a virtual severed blood vessel using forceps and a suture (micro-anastomosis). Microsurgery makes it possible to demonstrate several facets of the simulation algorithms, including the deformations of the blood vessel and the suture, and the collisions and interactions between the vessel, the forceps, and the suture. Validation of the overall microsurgery system is based on subjective analysis of the simulation's visual realism by different users.