A general theory for the calculation of the elastic constants of molecular crystals has been developed within the pair-potential rigid-molecule approximation. Interatomic rather than intermolecular interactions are considered explicitly, thus taking more angular dependence into account. Model calculations for CO2have been carried out, the results being in good agreement with those obtained using the crystal packing programme PCK83, with the same set of potentials. Both methods yield lower values than the corresponding intermolecular potential calculations for thec11,c12andc44tensor components of CO2.