Abstract Recently, it has been found by the present authors that microplastic deformation can be produced in zinc polycrystalline plates if the temperature of the specimen is changed by less than 1 K. This deformation showed itself as a sharp drop in the resonance frequency of the zinc plate when it is cooled below room temperature. The drop was followed by an increase in the frequency upon further cooling, thus producing a relative minimum at about 230 K. The effect was attributed to the internal stresses produced by the strong anisotropic thermal expansion of the randomly oriented hexagonal zinc crystals. In the present work the study was extended to other polycrystalline h.c.p. metals, namely, cadmium and cobalt. In cadmium, owing to its strong anisotropic thermal expansion, a behaviour similar to that observed in zinc was detected while, in cobalt, where the thermal anisotropy is weak, a slight convexity occurs in the frequency—temperature curve. A new mathematical model was proposed to account for this behaviour in h.c.p. metals. For zinc, the model consists of two terms. The first is a linear elastic term which represents the influence of thermal agitation on the distances between atoms. The second is an exponential term which represents the, increase in dislocation density due to microplastic deformation. For cadmium, in addition to these two terms, a third term is added to represent a thermally activated relaxation process which takes place between 100 and 200 K. The mathematical model fits the experimental results very satisfactorily, showing that the structural processes giving rise to the observed frequency drop are correctly understood.