A constitutive theory for hygrothermoelasticity in anisotropic media is developed. The first and second laws of thermodynamics are extended to include moisture diffusion. The resulting equations are capable of fully coupling the deformation field with hygroscopic phenomena and temperature distributions. It is shown that, upon decoupling, the present theory reduces to the well-known equations of diffusion, heat conduction, and elasticity. With appropriate numerical schemes, the coupled equations can be applied to matrix-fiber composite structures subject to hygrothermal environments. As a step toward major numerical applications to aerospace and other structures, the present paper demonstrates one-dimensional finite element solutions. The results predicted by the theory appear to be quite satisfactory.