Investigation of weakly swirling flow in a model of blood vessel with asymmetrical stenosis has been performed using both experimental flow measurement techniques (ultrasound Doppler) and computational fluid dynamics methods. A special attention was paid to getting data for the length of reverse-flow zone occurring past the stenosis. It was established that the laminar steady-state flow model was acceptable for numerical analysis of flow past the given geometry stenosis at the Reynolds number values less than 300. At higher values of this parameter, application of the semi-empirical k-ω SST turbulence model was preferable. It was shown that flow swirl was able to lead to an increase of the reverse-flow zone.