We simulate the intravasation of liquid distention media into the systemic circulation as it occurs during hysteroscopy and transurethral resection of the prostate. A linear network flow model is extended with a correction for non-newtonian blood behaviour in small vessels and an appropriate handling of vessel compliance. We then integrate a fast lookup scheme in order to allow for real-time simulation. Cutting of tissue is accounted for by adjusting pressure boundary conditions for all cut vessels. We investigate the influence of changing distention fluid pressure settings and of the position of tissue cuts. Our simulation predicts significant intravasation only on the venous side, and just in cases when larger veins are cut. The implemented methods allow the realistic control of bleeding for short-term and the total resulting intravasation volume for long-term complication scenarios. While the simulation is fast enough to support real-time training, it is also adequate for explaining intravasation effects which were previously observed on a phenomenological level only.