Arterioles and microvascular venules often show rhythmic spontaneous changes in diameter, called vasomotion. In this study, we analyze the possibility that vasomotion originates from the activity of the local myogenic mechanism. This analysis uses an original mathematical model of the peripheral circulation. The peripheral vascular bed has been represented as a series of three consecutive segments, each characterized by its value of vascular resistance per unit weight of tissue. The internal radius of the vessels in the last two segments, and hence their hydraulic resistance, has been assumed to be affected by the local myogenic response of the vascular smooth muscle. This dependence has been reproduced using the Laplace law. Both the static and dynamic (i.e. rate-dependent) components of the myogenic response have been included in the model, in accordance with recent experimental results. Simulations demonstrate that rhythmic, self-sustained oscillations can develop when the dynamic component of the myogenic response of terminal arterioles is much greater than that of more proximal microvessels. A moderate increase in arterial pressure favors the occurrence of oscillations, whereas vasodilatory stimuli tend to suppress vasomotion and contribute to the stabilization of vascular diameters.