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A detailed theoretical analysis and careful experimental measurement of the phase distribution of two-dimensional Josephson junctions are reported. The current density distribution along the junction contour, which provides the boundary conditions of the problem, is obtained through analog modelling by the electric field distribution in an electrolytic bath. The dependence of the critical supercurrent upon the applied magnetic field has been considered for square cross-type junctions. The experiments performed on Nb-NbxOy-Pb samples confirm unambiguously all the peculiar features predicted by the theoretical analysis.