J. Kent Harbaugh and D. Stroud, Department of Physics, The Ohio State University, Columbus, Ohio 43210

We calculate the current-voltage characteristics and critical current I_c^{array} of an array of Josephson-coupled superconducting wires. The array has two layers, each consisting of a set of parallel wires, arranged at right angles, such that an overdamped resistively-shunted junction forms wherever two wires cross. A uniform magnetic field equal to f flux quanta per plaquette is applied perpendicular to the layers. If f = p/q, where p and q are mutually prime integers, I_c^{array}(f) is found to have sharp peaks when $q$ is a small integer. To an excellent approximation, it is found in a square array of n^2 plaquettes, that I_c^{array}(f) is proportional to (n/q)^{1/2} for sufficiently large n. This result is interpreted in terms of the commensurability between the array and the assumed q X q unit cell of the ground state vortex lattice.