The results for blood flow in the carotid artery bifurcation on the basis of numerical simulation of Navier-Stokes equations are presented in this study. Four cases of carotid bifurcation are considered: common carotid artery (CCA) bifurcation without stenoses and cases with one, two and three stenoses are also presented. The results are obtained by performing numerical simulations considering one pulse wave period based on the finite volume discretization of Navier-Stokes equations. The structures of the flow around the bifurcation are obtained and the deformation of the pulse wave from common carotid artery (CCA) to the internal carotid artery (ICA) and external carotid artery (ECA) is traced. The axial velocity and wall shear stress (WSS) distribution and contours are presented considering the characteristic time points. The results of the WSS distribution around the bifurcation allow a prediction of the probable sites of stenosis growth.