The simulation of blood flow in the cardiac system has the potential to become an attractive diagnostic tool for many cardiovascular diseases, such as in the case of aneurysm. This potential could be reached if the simulations were to be completed in hours rather than days and without resorting to the use of expensive supercomputers. Therefore we have investigated a possibility of accelerating medical computational fluid dynamics (CFD) simulations using graphics processing units (GPUs). Our results for the 3D blood flow in the human abdominal aorta show that by transferring only a part of the computations (linear system solvers) to the GPU, it is possible to make the typical CFD simulations three to four times faster depending on the CFD model being used. Since these simulations were performed on widely available GPUs that had been designed as mass-market PC extension cards, our results suggest that porting larger parts of CFD to GPUs could really bring the technology into hospitals.