The cytoplasm of cultured human lymphoblasts has a particular organization. A ring formed by actin and myosin delimits a region of the cell where an active membrane veil forms. Depolymerization of the microtubular cytoskeleton releases this ring, which then oscillates between the two poles of the cell. This periodic movement has been studied and described with great precision. We have used these experimental results to model the oscillation of the ring. We have constructed a system of reaction-diffusion equations designed to stimulate the behaviour of the actin and have considered three variables representing, respectively, the proteins involved in actin nucleation, F-actin bound to the plasma membrane and free F-actin, part of which is assumed to constitute the ring, together with myosin. There are two types of results. First, from a theoretical point of view, we have succeeded in simulating a perfect back-and-forth movement of a wave. Second, this model suggests that actin alone, by virtue of its intrinsic properties, can generate an oscillatory movement within the cell, without the need for other oscillators.