High heat flux components in fusion reactors will experience inelastic strains resulting from swelling, creep, and thermal expansion. Additionally, because of thermal and irradiation creep, the stresses will redistribute during the lifetime of the component. Current proposals for fusion first walls and divertors include structures fabricated by bonding two different metals together. The plasma side material is chosen to minimize sputtering; the coolant side material is chosen to maximize heat transfer. The structural response of such a design is not well known. Accordingly, a one dimensional inelastic stress analysis of a thin walled shell element has been performed. The stress analysis can include temperature dependent material properties, radiation induced swelling, thermal and irradiation creep, and thermal expansion. Furthermore, a simple equation has been derived for the case of a duplex plate constrained from bending. The stress distribution through the plate is followed with time. It is shown that the initial stress distribution evolves with time until some near steady state distribution is approached. The evolution is dependent on swelling and particularly on creep.