Abstract The elasticity of a polycrystalline aggregate is expressed in terms of the elasticity of the individual grains. The stress within each grain is estimated with the aid of an analysis of the stress distribution around a spherical cavity in an isotropic medium. The strain within each grain is expressed in terms of the average stress in the polycrystal as a whole by pseudoelastic constants which are related to the actual elastic constants. The calculated elasticities for physical tests and for x-ray diffraction measurements in polycrystals are given for a few cubic metals.