This paper deals with the numerical solution of blood flow in a channel with narrowing and bypass. The paper is divided into a numerical simulation of fluid flow in a constricted channel without bypass and a numerical study of a narrowed channel with bypass with different connection angles. This part deals with the values of the connection angle between 30 and 60  \(^\circ \) C. The mathematical model is based on the three-dimensional generalized Navier-Stokes equations, where either a Newtonian or a non-Newtonian rheological model is considered. In the case of non-Newtonian models, the Carreau model and the Power law model are used to solve the shear nature of the blood flow. Numerical results are compared by measuring wall shear stress and wall pressure distribution. Numerical tests are performed to verify whether and how much such a change depends on the angle of connection or on the generalized Newtonian model used. Numerical results are obtained using OpenFOAM and are compared for all values of the bypass connection angle and selected rheological viscosity models.