We have investigated the mechanical properties of semiconducting clathrate frameworks composed of group 14 elements carbon, silicon, germanium, and tin. The bulk moduli, Young's moduli, and elastic anisotropies of 13 structurally different clathrate frameworks were determined using quantum chemical methods. The predicted elastic properties were compared to the properties of diamondlike, dense alpha-phases and experimentally known semiconducting group 14 clathrate structures. The predicted bulk and Young's moduli of the studied carbon, silicon, germanium and tin frameworks suggest them to possess low compressibility and high stiffness, which are almost comparable to the diamondlike, dense alpha-phases of the elements. In particular, the studied microporous clathrate frameworks exhibit remarkably low elastic anisotropy, being clearly more isotropic than the denser alpha-phases.