During therapeutic hysteroscopy and transurethral resection of the prostate, intravasation of the liquid distension media into the vascular system of the patient occurs. We present a model which allows the integration of the intravasation process into surgical simulator systems. A linear network flow model is extended with a correction for non-Newtonian blood behavior in small vessels and an appropriate handling of vessel compliance. We employ 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. In addition, we quantify the intravasation occurring with different approaches of fluid control, and we compare the performance of direct and iterative solvers applied to the non-linear system of the compliant model. 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 of 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.