Colloidal suspensions of platelets are known, experimentally, to show a variety of phenomena reflecting the interplay of their Oseen-Frank elastic constants and surface tension effects [1, 2]. We have previously determined the Frank elastic constants of thin hard platelets by Monte Carlo simulation [3] and have recently extended this work to non-zero thickness [4], in both cases comparing with theoretical predictions. As expected, the bend elastic constant K3 is at least an order of magnitude smaller than the other two; the results are in reasonable agreement with experiment. We have also examined the phases of thin hard platelets confined between hard flat walls, observing surface-induced ordering and capillary condensation of the nematic phase.