This research proposes the self-similarity design concept of flexible mechanisms by studying the out-of-plane, piston motion of a compliant device. Self-similar compliant mechanisms can be formed by connecting flexible units of scaled-down, identical geometry in series and/or parallel. We study a folded-architecture, compact mechanism class formed of multiple flexible, circular, and concentric segments that are serially connected. The device is capable of producing large displacements by summing the small deformations of its units. A simple analytical model is derived, which predicts the mechanism piston compliance/stiffness in terms of configuration, geometry, and material parameters. Experimental testing of a prototype and finite element simulation of various designs confirm the validity of the mathematical model. Several particular designs resulting from the generic architecture are further characterized based on the analytical model to highlight the mechanism stiffness performance and the way it scales with its defining parameters and unit stiffness.