# Article

**Summary:**

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.