FlexEOP is a method to create flexible electroosmotic pumps that are fully composed of flexible materials, facilitating shape-changing actuators with high flexibility and self-containment. We demonstrated the design space of FlexEOP, including shapechanging display on flexible strips, panels, and curved surfaces, and a novel design of soft robotic fiber. We envision future applications including wearable tactile devices, curved shapechanging displays, and multi-degree-of-freedom self-contained soft robotics.