  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) \propto (n/q)^{1/2} for sufficiently large n.
This result is interpreted in terms of the commensurability between the array
and the assumed q \times q unit cell of the ground state vortex lattice.
