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The realization of concurrently largely expandable and selectively rigid structures poses a fundamental challenge in modern engineering and materials research. Radially expanding structures in particular are known to require a high degree of deformability to achieve considerable dimension change, which restrains achievable stiffness in the direction of expanding motion. Mechanically hinged or plastically deformable wire-mesh structures and pressurized soft materials are known to achieve large expansion ratios, however often lack stiffness and require complex actuation. Cardiovascular or drug delivery implants are one example which can benefit from a largely expandable architecture that is simple in geometry and intrinsically stiff. Continuous shell cylinders offer a solution with these properties. However, no designs exist that achieve large expansion ratios in such shells when utilizing materials which can provide considerable stiffness. We introduce a new design paradigm for expanding continuous shells that overcomes intrinsic limitations such as poor deformability, insufficient stiffness and brittle behaviour by exploiting purely elastic deformation for self-expandable and ultra-thin polymer composite cylinders. By utilizing shell-foldability coupled with exploitation of elastic instabilities, we create continuous cylinders that can change their diameter by more than 2.5 times, which are stiff enough to stretch a confining vessel with their elastic energy. Based on folding experiments and analytical models we predict feasible radial expansion ratios, currently unmatched by comparable cylindrical structures. To emphasize the potential as a future concept for novel simple and durable expanding implants, we demonstrate the functionality on a to-scale prototype in packaging and expansion and predict feasible constellations of deployment environments. [ABSTRACT FROM AUTHOR]