This research proposes using the fractal concept to the design of flexible mechanisms by studying the out-of-plane, piston motion of a fractal-configuration device. Multiple flexible, circular and concentric segments are serially connected in a folded architecture to form a compact mechanism that 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 confirm the mathematical model validity. 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.