Phase contrast MRI allows access to tri-directional encoded velocity information and therefore, measurement of flow in the human hemodynamic system. The aim of this work was to investigate whether this technology could be applied to support the grading of stenosis in mid-size arteries. Using a specially constructed flow phantom and a stenosis model with tube diameter of 5 mm and 8 mm and a stenosis of 50%, experiments at different flow rates (180–640 ml/min), slice thickness (1–4 mm), field strength (1.5 and 3.0 T), and multi-slice as well as 3D volume acquisition were performed. The observations were assessed visually and evaluated by signal-to-noise (SNR) ratios in regions before and after the stenosis. The obtained results show that examinations should be performed at high field (3.0 T) and at flow rates up to 500 ml/min without hampering the measurements by areas of signal loss. In comparison, no detectable differences in the flow patterns of the two acquisition schemes could be observed. However, the SNR was higher using the 3D volume acquisition and thick slices. In summary, 3D PC-MRI of mid-size vessels with stenosis is feasible for certain flow rates. The presented results could be seen as guidance for in vivo situations to assess if an examination of a patient is reasonable in terms of outcome.