The physical mechanism of piezoelectricity arising in crystals of all pyroelectric classes is described and discussed in detail. The piezoelectric effect of these crystals is postulated to be a consequence of changes in their spontaneous polarization under the impact of external forces (electric fields, mechanical stresses). This study shows which piezoelectric coefficients do exist in pyroelectric crystals. Both the direct piezoeffect--generation of electric polarization under mechanical stresses--and the inverse piezoeffect--crystal deformations caused by the application of an electric field--are considered. Specifically, the analysis performed suggests that crystals of classes 6, 4, and 3 may lack d14 and d25 piezo modules, the existence of which is, in principle, allowed by the symmetry of the crystals, but which do not actually exist because of the accidental cancellation of requisite "piezo-generating" elastic compliance coefficients.