Elastic constants and the Poisson ratio of defect-free hard-disk solid are determined by two independent methods: (1) analysis of the box side fluctuations in the N-p-T ensemble with variable box shape and (2) numerical differentiation (with respect to strain components) of the free energy computed in the N-V-T ensemble; N, p, V, and T denote the number of particles, the pressure, the volume, and the temperature, respectively. The efficiency of the applied methods is compared. It is shown that reasonable estimates of the elastic properties can be obtained by studying small systems in the N-p-T ensemble and that the singular behavior of the elastic constants near close packing is well described by the free volume approximation; the coefficients of the leading singularities are estimated. (C) 2003 American Institute of Physics.