This study proposes a mathematical model for studying stability of arteries subjected to a longitudinal extension and a periodic pressure. An artery was considered as a straight composite beam comprised of an external thick-walled tube and a fluid core. The dynamic criterion for stability was used, based on analyzing the small transverse vibrations superposed on the finite deformation of the vessel under static load. In contrast to the case of a static pressurization, in which buckling is only possible if the load produces a critical axial compressive force, a loss of stability of arteries under periodic pressure occurs under many combinations of load parameters. Instability occurs as a parametric resonance characterized by an exponential increase in the amplitude of transverse vibrations over several bands of pressure frequencies. The effects of load parameters were analyzed on the basis of the results for a dynamic and static stability of a rabbit thoracic aorta. Under normal physiological loads the artery is in a stable configuration. Static instability occurs under high distending pressures and low longitudinal stretch ratios. When the artery is subjected to periodic pressure, an independent increase in the mean pressure, amplitude of the periodic pressure, or frequency, most often, but not always, increases the risk of stability loss. In contrary, an increase in longitudinal stretch ratio most likely, but not certain, stabilizes the vessel. It was shown that adaptive geometrical remodeling due to an increase in mean pressure and flow does not affect artery stability.