Computer assisted surgery (CAS) systems can provide different levels of assistance to a surgeon during training and execution of a surgical procedure. This is done through the integration of : measurements taken on medical images; computer graphics techniques; and positioning or tracking mechanisms which accurately locate the surgical instruments inside the operating site. According to the type of assistance that is provided to the surgeon, CAS systems can be classified as: Image guided surgery systems; Assistant robots for surgery; and Training simulators for surgery. In this work are presented the main characteristics of CAS systems. It is also described the development of a computer simulator for training on Transurethral Resection of the Prostate (TURP) based on a computer model of the prostate gland which is able to simulate, in real time, deformations and resections of tissue. The model is constructed as a 3D mesh with physical properties such as elasticity. We describe the main characteristics of the prostate model and its performance. The prostate model will also be used in the development of a CAS system designed to assist the surgeon during a real TURP procedure. The system will provide 3D views of the shape of the prostate of the patient, and the position of the surgical instrument during the operation. The development of new computer graphics models which are able to simulate, in real time, the mechanical behavior of an organ during a surgical procedure, can improve significantly the training and execution of other minimally invasive surgical procedures such as laparoscopic gall bladder surgery.