The paper describes aspects of the application of numerical simulation of fluid flows in clinical medicine with interventions on the human vascular system. The modeling method used in the study is verified using the data of the doppler sonography of the patient underwent vascular replacement. It was shown that the deviation between the numerical experiment and the clinical data - pressure curves at the inlet and outlet of the studied vessel, is 20%. The obtained quantitative characteristics of the flow: peak systolic velocity, final diastolic velocity, minimum diastolic velocity, resistivity index, pulsatility index, systole/diastole index are comparable between verification and experimental data. Thus, for the proximal site of the clinical vessel the corresponding indices were 96.5 cm/s; 4.5 cm/s; 36.2 cm/s; 1.05; 11.5; 21.3. For simulation, 107.9 cm/s; 4.44 cm/s; 43.9 cm/s; 1.05; 12.0; 24.3. In addition, the work describes the application of tested method in two clinical vascular prostheses "KemAngioprotez" for the assessment of zones of increased shear stress and, thus, the risk of thrombus formation. It is shown that the distribution of critical zones corresponds to zones of anastomosis between prosthesis segments, which may be a potential location for optimization of the device.