The one-dimensional model of the blood flow in large vessels is considered. The non-Newtonian nature of blood is modeled by the friction force and Boussinesq coefficient value. The power law rheological model of fluid is used. The comparison with the models of blood as ideal and Newtonian fluid is realized. The nonlinear problems of single-pulse propagation in a single vessel and in a vessel with bifurcation are considered. It is demonstrated, that non-Newtonian effects play an important role in the obtained solutions.