Membrane materials can effectively be used as hinges in origami-inspired engineering designs. Because this application of membrane materials is recent, an understanding of how these materials perform under repeated cyclic loading in these conditions needs to be defined. This research reports cyclic testing of membrane hinges for origami-inspired engineering designs. When incorporating membrane hinges, the life of the membrane material should be considered to ensure that the device will withstand the anticipated number of cycles. Testing includes three polymers, a fiberglass, and three steels (including a stainless steel mesh) with 0.076 mm thickness. They are tested under fully reversed loading conditions with a constrained minimum radius. Because of the low number of cycles anticipated in most deployable origami systems, the membrane hinges were tested up to 10,000 cycles. The number of cycles until visual damage and the number of cycles until complete failure were observed and recorded. The polymers and fiberglass exceed 10,000 cycles and cycle data is provided for the metals. The work can be used to guide testing of membrane hinges for use in engineering applications or origami, including deployable space systems.