A compliant hinge for deployable membrane-like structures and other applications is provided. The compliant hinge generally includes a flexible intermediate portion having one or more enclosed contours connected by inner longitudinal segments along a longitudinal axis of symmetry. The enclosed contours are resiliently deformable in response to an in-plane load, including tension and shear forces. The compliant hinge allows for rotation, bending, and extension, and can interconnect rigid panels in tensioned precision structures and other applications.