To understand the “elastic softening” of Li–Si alloys for the development of Li-ion batteries, the effect of stress-induced change of entropy on the mechanical properties of lithiated materials is examined within the theories of thermodynamics and linear elasticity. An approach is presented whereby the change of Gibbs free energy is governed by the change of the mixture entropy due to stress-induced migration of mobile atoms, from which the contribution of the change of the mixture entropy to the apparent elastic modulus of lithiated materials is determined. The reciprocal of the apparent elastic modulus of a lithiated material is a linear function of the concentration of mobile Li-atoms at a stress-free state and the square of the mismatch strain per unit mole fraction of mobile Li-atoms.