When the temperature and/or moisture at the surfaces of a composite change suddenly, stresses will arise in the composite owing to the nonuniform diffusion of heat and moisture. Recent investigations have shown that under certain conditions the classical uncoupled theory of diffusion can significantly underestimate the coefficient of diffusion. The coupling between heat and moisture is an inherent part of the diffusion process that cannot be neglected on intuitive grounds. This investigation is an inquiry into the influence of antisymmetric boundary conditions on the magnitude of the hygrothermal stresses in a plate made of T300/5208 epoxy material, commonly used in graphite fiber-reinforced composites. Both moisture and temperature boundary conditions are considered. Because of the nonlinear character of the coupled equations, a finite-difference scheme is adopted. Numerical results involving time-dependent moisture, temperature, and stress distributions in the plate are displayed graphically; they show that the stresses derived from the coupled theory differ appreciably from the uncoupled results, both qualitatively and quantitatively. The hygrothermal stresses with coupling taken into account acquire an oscillatory character when the temperature on the plate is raised suddenly; this factor could contribute to material damage. In addition, antisymmetric boundary conditions can either raise or lower the stress levels, depending on time and the transient nature of the applied temperature.