The linear coupling of elastic deformations and solute diffusion in solids produces effects such as strain-induced diffusion and solute-induced dilatation. While this coupling also affects changes in certain material properties, many important physical effects must be described within a framework that includes the nonlinear coupling of the diffusion and deformation fields. The nonlinear coupling of these fields is developed using a continuum approach based in thermodynamics that considers the possible effects that might arise in elastic solids containing a mobile solute species. Among others, this coupling produces effects including point defect-related modulus variations, harmonic generation in acoustic waves, and diffusion in the presence of transient, equivoluminal strain fields.