We study by means of ab initio calculations the ideal tensile and shear strengths of the C-46 clathrate phase. While its bulk modulus and elastic constants are smaller than in diamond, its strength is found to be in all directions larger than the critical stresses associated with the diamond [111] planes of easy slip. This can be related to the frustration by the clathrate cage structure of the diamond to graphite instability under nonhydrostatic stress conditions [corrected] The criteria for designing strong materials are discussed.