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This paper deals with the numerical solution of Newtonian and non-Newtonian flows. The flows are supposed to be laminar, viscous, incompressible and steady. The model used for non-Newtonian fluids is a variant of the power-law. Governing equations in this model are incompressible Navier-Stokes equations. For numerical solution we could use artificial compressibility method with three stage Runge-Kutta method and finite volume method in cell centered formulation for discretization of space derivatives. The following cases of flows are solved: flow through a bypass connected to main channel in 2D and 3D and non-Newtonian flow through branching channels in 2D. Some 2D and 3D results that could have an application in the area of biomedicine are presented.
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