With the development of computers and numerical methods, the conditions for numerical modeling of complex flows such as blood flow in the arterial blood stream appeared. The aim of this work is to run a numerical simulation of blood flow through an arterial bypass. In this thesis is defined mathematical model of incompressible, isothermal, laminar, 3D pulsating flow inside a blood vessel with a rigid wall. Two geometrically different models of joining the bypass to a healthy part of the blood vessel were created and analyzed: a joint in the form of a knee and a joint in the form of a fork. The pulsatile blood flow was achieved by prescribing the time profile of the volume blood flow at the entrance to the domain and incorporating the Windkessel model with 3 elements as a boundary condition at the exit from the domain. The role of the Windkessel model is to consider the compliance of the blood vessel, the peripheral resistance of the microcirculation and the input impedance of the aortic valve. The intensity of oscillatory shear stress is considered by the product 𝑂𝑆𝐼 ∙ 𝜏𝑤, in which the OSI factor expresses the degree of change in the direction of wall shear stress, and 𝜏𝑤 represents the mean value of wall shear stress on the blood vessel wall. The amount of this product is used as a criterion for evaluating the conditions for the formation of hyperplasia (thickening of the blood vessel wall). The simulation was carried out in the OpenFOAM software package, while the results were analyzed in the ParaView and gnuplot. The simulation results show that due to the sudden change in blood flow direction and the existence of sharp edges, the wall shear stress values are higher in the case of the junction of the bypass and blood vessel in the form of a fork compared to the junction in the form of a knee. Also, in the case of joint in the form of a fork, values of the product 𝑂𝑆𝐼 ∙ 𝜏𝑤 are several times higher in the area where the occurrence of hyperplasia is expected in real conditions.