Lattice Monte Carlo simulations and the contact distribution method are used to analyze the force of interactions between two undersaturated polymer layers in good solvents. The net force between the surfaces, resulting from a competition between bridging attraction and steric repulsion, is obtained unambiguously for coverages Gamma ranging from 0 to the saturation coverage Gamma (0) The sizes and the number of the bridges are in qualitative agreement with previous scaling analysis,. but a number of quantitative differences important in practice emerge from the simulations. While the bridges may be considered as independent elastic tethers at low coverages, steric interactions begin to exert influence for coverages as low as Gamma approximate to 0.3 Gamma (0). Comparison of the results of the simulations with numerical mean-field calculations based on second-order Markov chains (i.e., without backfolding) shows good agreement with some of the structural features of the polymer layer, but important discrepancies regarding the force of interaction exist for all values of Gamma/Gamma (0). Whereas the mean-field calculations predict that the crossover from attraction to steric repulsion occurs only near saturation, the simulations show the crossover to occur at a much higher degree of undersaturation (i.e., Gamma/Gamma (0) approximate to 0.85). The simulation method used provides an opportunity to scrutinize systematically the details of the mean-field theory and to refine the theory for providing better guidance in practice. The results presented here focus on a low molecular weight chain (N = 200). Whether the asymptotic behavior for very long chains predicted by the scaling/free energy functional approach is obtained still needs to be tested.