A new approach for the equilibrium deformation of three-dimensional chains, that are bigrafted to parallel planes is presented. The underlying lattice Monte Carlo algorithm is the bond fluctuation model. In addition to the excluded-volume interaction of this a priori athermal algorithm, we incorporated external potentials in order to enable direct detection of forces. The whole deformation process is split up into a series of separate steps. Each step consists of a generation process and subsequent relaxation procedures. Stress and strain an simultaneously calculated as time-averaged quantities of sufficiently equilibrated systems. Stress-strain relations ranging from compression to the highly stretched regime were simulated by variation of both chain length, N, and grafting density, sigma. In the high-density limit the simulation data agree perfectly with a simple one-dimensional theory. The N and sigma dependency of the distance, h(0)(N, sigma), of grafting planes at vanishing force is in qualitative agreement with theoretical predictions for an intermediate regime of sigma. The simulated force-length relations an in satisfactory agreement with current scaling predictions.