The paper describes one of many issues concerning the human circulatory system. The simulation of blood flow through an artificial aortic heart valve using the finite element method (FEM) is the main subject of the paper. The studies aim to verify the performance of mechanical aortic valves of two types, i.e. bileaflet (BIL) and trileaflet (TRI) valves. The blood was modelled as Newtonian and non-Newtonian. Although the design of our TRI valve is preliminary and needs to be optimised, our results highlight some advances of such a valve geometry. This is manifested mainly by a central blood jet, contributing to more physiological blood flow and decreasing the risk of haemolysis. The central flow minimises the risk of leaflet dislocation. In addition, lower stresses extend the durability of the valve. However, the TRI valve geometry has also disadvantages, for instance, the occurrence of small peripheral streams or relatively low effective orifice area. The valves' performance was assessed by means of the reduced stress in the valves, the shear stress in the aortic wall, flow velocity field, and the effective orifice area. The maximum von Mises stress for the BIL valve leaflets is 0.3 MPa, and for the TRI valve: 0.06 MPa. The maximum flow velocity for the BIL valve is 4.52 m/s for 40° and for the TRI valve is 5.74 m/s. Higher shear stress is present in the BIL (151.5 Pa) than for the TRI valve (49.64 Pa).