This paper discusses the dependence of IJ, the maximum zero-voltage current, on magnetic fields for a series of Josephson junctions of differing size when compared with λJ, the Josephson penetration depth. The experimental results are in excellent agreement with the calculations; in particular, for junctions with L≫λJ, the Meissner effect and overlapping vortex structure are clearly demonstrated. The current density distributions are also shown. Finally, the implications of size dependence for tunneling cryotron devices is discussed. © 1969 The American Institute of Physics.