This article discusses selected aspects of modelling blood flow in the arteries. The method of reproducing the variable-in-time geometry of coronary arteries is given based on a sequence of medical images of different resolutions. Within the defined shapes of the arteries, a technique of generation of numerical meshes of the same topology is described. The boundary conditions and non-Newtonian rheological models used in blood flow are discussed, as well as the description of blood as a multiphase medium. The work also includes a discussion of tests on the phantom of the carotid artery for the accuracy of measurements made using ultrasonography.