Compliant energy storage has not kept pace with flexible electronics. Herein we demonstrate a technique to reinforce arbitrary battery electrodes by supporting them with mechanically tough, low-cost fibrous membranes, which also serve as the separator. The membranes were laminated to form a full cell, and this stacked membrane reinforcement bears the loads during flexing. This technique was used to make a high energy density, nontoxic Zn–MnO2 battery with printed current collectors. The Zn and MnO2 electrodes were prepared by using a solution-based embedding process. The cell had a nominal potential of 1.5 V and an effective capacity of approximately 3 mA h cm−2. We investigated the effect of bending and fatigue on the electrochemical performance and mechanical integrity of the battery. The battery was able to maintain its capacity even after 1000 flex cycles to a bend radius of 2.54 cm. The battery showed an improvement in discharge capacity (ca. 10 %) if the MnO2 electrode was flexed to tension as a result of the improvement of particle-to-particle contact. In a demonstration, the flexible battery was used to power a light-emitting diode display integrated with a strain sensor and microcontroller.