We study a percolating network of highly hysteretic Josephson junctions in which each junction is modelled as a piecewise-Ohmic hysteretic device. At the percolation threshold, the average voltage drop across a network on a large L × L grid is assumed to fall to zero as V ∼ (I -Ic(L))η as the applied current is reduced to the critical current Ic(L). Our finite-size Monte Carlo study gives the value η = 2.0±0.1. This value is remarkably close to the result η=2 obtained by a scaling analysis of a continuum version of the model. © 1988.