We propose Reconfigurable Umbrella Meshes (RUMs), a new class of preassembled deployable structures. A RUM has a compact rest state that can be easily altered to deploy into different bending-active 3D target shapes. RUMs consist of elastic beams and rigid plates connected by hinge joints and can be assembled in a stress-free fabrication state. The key principle of a RUM is that it encodes the desired deployment shape in the height distribution of its constituent cells. Reconfigurability is achieved by introducing sliding joints to connect the elastic beams with the rigid plates to allow adapting the cell heights. We demonstrate that even for small variations in the cell heights, RUMs can capture a diverse range of shapes. Assembled from identical cells that can be mass-produced, a RUM can deploy into several desired shapes, which makes them well suited for reusable temporary structures. We provide a computational design tool based on physical simulation, where users can interactively edit cell heights to explore achievable deployed shapes. Numerical optimization enables designers to easily navigate between the reconfigurable design parameters and the deployed shape space. We validate our approach with a physical prototype and demonstrate its various deployed states.