Understanding the nature of pulsatile flow is an important issue in haemodynamics, especially the initiation and progression of vascular disease. The geometry of a non-circular vessel was idealised to an elliptical cross-section, and the dynamic properties of the flow were calculated for a physiological waveform. The Fourier harmonics for a common carotid waveform were determined, and the velocity profile and wall shear stress were calculated from the superposition of the individual contributions from each harmonic. The effects of ellipticity on the flow pattern were found to be significant. The velocity profile along the major axis of the elliptical cross-section developed a flattened peak, which widened as the vessel became more elliptical. Wall shear stress demonstrated an angular dependence in elliptical vessels, where the point of minimum shear stress was located at the end of the major axis. Comparison with a cylindrical vessel demonstrated a 3% decrease in peak wall shear stress (τ = 2.96, N·m<sup>–2</sup>) at the end of the major axis, and 10% in the mean wall shear stress (τ = 0.44 N· m<sup>–2</sup>), for an elliptical vessel (Ε = 0.8). The temporal average wall shear stress, which has been associated with atherogenic sites, also displayed a minimum at the end of the major axis that decreased with more elliptical cross-sections.