In this paper, a solution to the numerical simulation of blood flow in the human thoracic aorta is presented. In vivo measurements of pulsewave waveforms were performed and used as the initial condition for numerical calculations. Equations resulting from the analysis of the general mass and momentum balance for blood flow were used for the description of aortal haemodynamics. The system of differential equations has been solved with the method of characteristics, which is often used in hydrodynamic problems. Numerical simulations were employed for the cases of three people of differing ages. As a result, time-dependent profiles of blood pressure and velocity as well as deformation of the arterial wall were determined.