Ab initio and empirical force field methods are used to simulate the loading of a large graphene membrane under an indenter analogous to an atomic force microscope tip. From these calculations we attempt to resolve ambiguities around determination of the elastic constants of graphene from such indentation experiments. We investigate the effect of the formation of wrinkles and more importantly the applicability of modelling the membrane as a continuous elastic sheet. By comparing empirical potential and large scale density functional theory calculations we have also assessed the performance of classical potentials in describing bending in this system. We find that the in-plane Young's modulus deduced from the indentation simulations using the classical expression for a clamped elastic membrane under a central point load is not consistent with that calculated directly from the in-plane stress-strain curve.