Monte Carlo simulations of the fcc phase of polydisperse hard spheres near close packing are reported. An experimental equation of state (EoS) is determined numerically in the NpT ensemble with variable shape of the periodic box. The close packing volume extrapolated from the obtained data shows a good agreement with earlier experiments performed by other methods. A new theoretical EoS, based on the free volume approximation, is proposed. The modified EoS fits experimental data for polydisperse hard spheres better than the approximation used before.