When studying the oscillatory flow in different types of blood vessels it is very important to know what type of the blood viscosity model has to be used. In general the blood viscosity is defined as a shear-thinning liquid, for which there exist different shear-dependent models, for example the Carreau model, which represents the viscosity as a non-linear function of the shear-rate. In some cases, however, the blood viscosity could be regarded as constant, i.e., the blood is treated as Newtonian fluid. The aim of the present work is to show theoretically and numerically some approximate limits of the Newtonian model application, when the blood vessel is assumed as a 2D straight tube. The obtained results are in agreement with other authors' numerical results based on similar blood viscosity models.