Lattice Monte Carlo simulations are used to analyze the normal force induced by interacting polymer chains between an athermal plane and an adsorbing plane in an athermal (good) solvent. The simulations are carried out under conditions of "restricted equilibrium" in which the amount of polymer in the system is not allowed to fluctuate. The results are compared with numerical, lattice mean-field calculations. We observe that mean-field theory usually overestimates the magnitude of the force. A substantial improvement in the comparison is obtained when interpreted with respect to properties of the corresponding unconfined layer at equilibrium with the bulk solution. For instance, in the case of high coverage, simulations and numerical mean-field theory are in good agreement at the same relative coverage, e.g., the same ratio of surface coverage to saturation coverage. Comparison with asymptotic scaling predictions does not yield unequivocal results for these chain lengths, but the results are roughly consistent with the nontrivial (-3) power law. A brief analysis of the compression of two layers against each other shows a strong similarity with the main results of this work when the surfaces bear an excess of adsorbed polymer chains (i.e., high coverage).