The dynamics of an elastic plate subject to a ''tectonic'' stress field and controlled by finite strength boundaries is studied, following the stress relaxation in a Maxwell asthenosphere due to a long sequence of dislocation events, localized on two antitethic transform boundaries. The model is plane bidimensionals and each dislocation events cutting the whole strike of the boundary, is interpreted as a sequence of ''earthquakes.'' The time of each dislocation event is determined as the time when the overall stress field reaches given threshold values on each boundary. If two boundaries only are considered, a stationary dislocation cycle is attained only if events on the two boundaries release opposite stress drops; if this is not the case, very slow diffusion of stress takes place in the medium, well beyond the two boundaries, and a stationary regime is not achieved even after a time lag greater than the age of the Earth. A periodic boundary model is then devised, which avoids introducing plates with infinite width. In this second model, stationary dislocation cycles are obtained even if the strength values of the antitethic boundaries are different from each other. From these simulations of the earthquake cycles, inference could be drawn, in principle, on tectonic parameters, and a formal equivalence can be stated between an elastic lithosphere affected by boundary earthquakes and a viscoelastic continuum lithosphere, subjected to the same tectonic stress field. Even if this plate model cannot be applied to any real plate of the Earth, nevertheless, the role of the finite widths of plates and of stress diffusion from very distant boundaries is proven to be important in modeling the seismic cycle and the deformation of plates. However, the extreme sensitivity of the model from very distant features and the trade-off existing between the long-time and the long-distance behavior imply that horizontally stratified, two-dimensional dislocation models cannot be profitably employed to simulate the seismic cycle in realistic situations. ¿ American Geophysical Union 1989