From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size1-4. Historically, two main strategies have been used to design deployable systems. The first and most frequently used approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract5-7, occasionally locking in place through bistable elements8,9. The second strategy makes use of inflatable membranes that morph into target shapes by means of a single pressure input10-12. Neither strategy, however, can be readily used to provide an enclosed domain that is able to lock in place after deployment: the integration of a protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape13-15. Here we draw inspiration from origami-the Japanese art of paper folding-to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the metre scale, such as arches and emergency shelters, providing a direct route for building large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces.