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This paper deals with a numerical simulation of the blood flow in bypass geometry, which consists of a main tube with a narrowing and its bridging by a bypass. Two different geometries of the bypass are considered, namely the classical bypass of the narrowed place and the second variant is the so-called S-type bypass. The optimal value of the connection angle of the bypass graft to the main channel is the subject of numerical testing in this work. Attention is focused on the values between 45 and 60 degrees. For the blood flow three relevant models are considered, namely Newtonian, Carreau and Power Law models. The numerical results are obtained using OpenFOAM and they are compared for all the considered types of geometry and for all values of the bypass connection angle and selected rheological viscosity models. [ABSTRACT FROM AUTHOR]