The stressed crystal that has been obtained during the crystallization process is considered with particular attention given to the comparative numerical analysis of composition and temperature gradients as the causes of the stressed state. The numerical calculations are referred to the directional solidification method. It is shown that the contribution of diffusion induced stresses to the total stressed state of a crystal in the growth process may be comparable to the contribution from thermostresses. In this article, as a consequence of the main thermodynamical laws the relations obtained by Larche´ and Cahn [Acta Metall.21, 1051 (1973)] are generalized to the case of a coupling dependence of elastic moduli on temperature and composition. The relations provide the important connection between the elastic modulus of compound materials measured using acoustic methods (at constant entropy and chemical potentials) and those that are used in practice (at constant temperature and composition). ©1995 American Institute of Physics.