Robotic systems for cardiac surgery have been introduced in clinical trials to facilitate minimally invasive techniques. Widespread use of surgical robotics necessitates new training methods to improve skills and continue practicing as the robotic systems are frequently being upgraded. Today, robotic training is performed on expensive animal models. An integration of a digital trainer with the two present robotic systems applied in coronary artery bypass procedures on beating heart requires real time simulation of tissue mechanics, sutures, instruments and bleeding. However, it requires no extra haptic device, since the robotic master is the haptic apparatus itself. By developing new data structures and parametric geometry descriptions we have demonstrated the possibility of obtaining surgical simulation on a standard PC Linux system. This technology is beneficial when simulation is exploited over a network with limited bandwidth, especially when it comes to the handling of soft tissue dynamics.