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With the remarkable increase in the performance of computers, techniques of computer simulation are widely applied. A computer simulation based on the finite element method and Monte Carlo method is applied to the problem of contact, and the conductance of a global model for contact is studied. The model consists of two unit cubes and a random interface between the cubes. More specifically, the two identical uniform conducting cubes are in contact across a pair of adjacent faces through a layer of thickness 2d subdivided into N x N small subsquares of which a randomly selected area fraction f has the same conductivity as the cubes (a clean-contact state), while the remaining area.fraction (1 - f) represents zero conductivity. The conductance of this global model for contact is computed and compared with previously published results. Particularly, when N, d, and f are changed, the behavior of the global conductance is investigated and discussed. It is clearly shown that because of extreme current concentration through the contact area the conductance does not decrease until f becomes close to zero.