In the last 30 years, thousands of basic or clinical studies have been devoted to atherosclerosis or to the problem of restenosis after angioplasty. In these studies, axial stresses in the vessel wall have received practically no attention, contrary to circumferential stress and purely biological aspects. Based on a recent article describing how arterial stenoses can induce a considerable increase in axial wall stress during flow systole in the region immediately proximal to the stenosis entrance, we have used a simple (theoretical) spring model and data available in the literature on the mechanical properties of arteries to investigate the relative wall elongations (axial strains) resulting from the systolic increases in axial stress generated by the stenosis. The model shows that high axial wall strains are tightly limited to the stenosis entrance if the axial wall forces generating the supplementary stress are strongly absorbed by the tissues surrounding the vessel. Inversely, if this absorption is weak, the zone of high strains extends over a longer vessel segment upstream of the stenosis entrance. The maximum strain value, which is always situated at the stenosis entrance, appears to be relatively independent of the presence or absence of surrounding tissues. The simulation also shows that in a 3 mm coronary artery presenting a 75% diameter stenosis, the axial strain at the stenosis entrance can exceed 10% at peak flow, depending on the respective axial elasticities of vessel wall and surrounding tissues. In a more severe stenosis, or in case of a pathologically high systolic pressure, the maximum strain value might even exceed 20%. Since abnormal axial strains have been shown to induce abnormal biological processes in smooth muscle cells cultures, it is quite conceivable that such axial strains are deleterious, at least in arterial segments whose length normally does not vary.