Assuming that the boundary planes in YBa 2 Cu 3 O 7−␦ can show a Josephson behavior, we establish the conditions required in epitaxial thin films to observe the modulation of the critical current by an applied magnetic field, as well as the possible forms of the modulated current. We report measurements carried out on two YBa 2 Cu 3 O 7−␦ films in the near vicinity of the critical temperature that show a partial modulation of their critical current. The comparison of the measured critical current changes to those predicted by the calculations shows that the experimental results are consistent with the Josephson modulation of the current carried by associations of weak links located in the boundary planes.