The paper is devoted to the considering of the mathematical model of blood flow in large vessels with non-Newtonian effects. The power law fluid is considered as a non-Newtonian model. The perturbation method for the solution of the initial problem for a nonlinear one-dimensional system of hemodynamic equations is proposed. The non-Newtonian model is compared with the models, where blood is considered as an ideal and Newtonian fluid. The solutions obtained can be used for the comparison of different blood models and for the testing of programs that implement numerical algorithms for packages, intended for computer simulation of blood flow.