Electrodeposition of lithium on lithium metal negative electrodes (anodes) of liquid cells produces filamentary deposits, resulting in poor cycling efficiency. Experiments suggest that filaments grow by extrusion of metal from the substrate, due to compressive stress introduced during deposition. A model is presented that explores the origin of stress generated in the anode during plating-stripping cycles. According to the model, plating or stripping reactions insert or remove lithium atoms at the interface between the metal and the solid electrolyte interphase (SEI) layer. Stress is induced by the resulting diffusion processes, with diffusion-induced strain accommodated by inelastic creep. Stress distributions during cycling are calculated, and are used in turn to predict curvature transients that would be measured in beam-deflection experiments. The calculations account for the three-dimensional surface morphology, since surface features that protrude above the surface plane do not contribute to curvature changes. Comparisons with recent curvature measurements demonstrate detailed agreement, with diffusion and creep parameters close to literature values. The results support the hypothesis that electrochemical reactions intrinsically generate stress. The model can serve as a framework for analysis of morphogical instability of the lithium anode interface in both liquid and solid-state cells.