The one-dimensional non-Newtonian model of blood flow, obtained by the averaging of three-dimensional hydrodynamic system is considered. The power law model with the parameters obtained from experimental data is considered as a model of non-Newtonian fluid. Initial-boundary-value problems for the system of nonlinear equations are stated and solved. The Lax - Wendroff scheme is used for the numerical calculations. Comparison with the ideal and Newtonian blood models is realized. It is demonstrated, that non-Newtonian effects play an important role and they must be taken into account in problems of modelling of blood flow in networks of blood vessels.