Abstract Thin sheets folded into three dimensional origami structures can be useful in various engineering applications. This work explores the stiffness of deployable origami tubes used as cantilevers. A unique “zipper” configuration is used to couple the tubes, which makes the systems easy to deploy, yet stiff for other deformation modes. The self-restricting geometry of the coupled tubes limits local deformations and makes the systems stiff for out-of-plane loading. The global deployment characteristics are explored using eigenvalue band-gaps, and indicate that tubes with lower sector angles are easy to deploy yet also stiffer for unintended motions. Cantilever analyses show that the geometry of the coupled tubes can significantly affect the stiffness, with some tube combinations having a high orthogonal stiffness throughout deployment, while others only having a high stiffness when fully deployed. Parametric studies are used to show optimal geometries for the coupled tubes that maximize the eigenvalue band-gaps and the stiffness throughout the deployment. The coupled tubes could serve applications such as adjustable robotic arms, and deployable space booms with a reliable extension sequence.