As compared with its radial wall displacement, axial wall displacement at the common carotid artery (CCA) carries independent clinical values, but its physical mechanisms are unclear. This study aims to investigate whether axial wall displacement at the CCA is solely from Young waves. A pulse wave propagation theory is utilized to identify two types of waves, Young waves, and Lamb waves, in an artery, and identifies two sources for axial wall displacement, wall shear stress and radial wall displacement gradient with a factor of the difference between axial and circumferential initial tension, which reveals the influence of axial initial tension on the waveform of axial wall displacement. Theoretical expressions are derived for calculating the waveforms of axial wall displacement and its two sources in the Young waves. With the measured pulsatile pressure and blood velocity at the CA of three healthy adults as the inputs, the waveforms of axial wall displacement in the Young waves are calculated at different values of axial initial tension and are found to greatly differ from their measured counterparts. As such, the Lamb waves may contribute to axial wall displacement at the CCA and the associated physical and physiological implications are discussed. Given the clinical values of axial wall displacement at the CCA, the Lamb waves may play a non-negligible role in determining arterial health and needs to be further studied for a comprehensive assessment of arterial wall mechanics.