Understanding the solvent-induced stresses in polymeric materials is of profound importance for drug release and soft robotics. This work presents an alternative method to obtain an analytical solution of solvent-induced stress in an elastic slab using the Moutier theorem under the framework of equilibrium thermodynamics and the elastic solution available in the literature. Using the analytical solution and the temporal evolution of the mass of organic solvents in polymeric slabs, we analyze the spatiotemporal evolution of the solvent-induced stress in the polymeric slabs and reveal the effects of the solvent transport on the stress evolution. The approach presented in this work provides a simple method to solve the decoupling problem involving diffusion and solvent-induced stresses.