Cylindrical Kresling origami structures are often used in engineering fields due to their axial stretchability, tunable stiffness, and bistability, while their radial closability is rarely mentioned to date. This feature enables a valvelike function, which inspired this study to develop a new origami-based valve. With the unique one-piece structure of origami, the valve requires fewer parts, which can improve its tightness and reduce the cleaning process. These advantages meet the requirements of sanitary valves used in industries such as the pharmaceutical industry. This paper summarizes the geometric definition of the Kresling pattern as developed in previous studies and reveals the similarity of its twisting motion to the widely utilized iris valves. Through this analogy, the Kresling structure’s closability and geometric conditions are characterized. To facilitate the operation of the valve, we optimize the existing structure and create a new crease pattern, RC-ori. This novel design enables an entirely closed state without twisting. In addition, a simplified modeling method is proposed in this paper for the non-rigid foldable cylindrical origami. The relationship between the open area and the unfolded length of the RC-ori structure is explored based on the modeling method with a comparison with nonlinear FEA simulations. Not only limited to valves, the new crease pattern could also be applied to microreactors, drug carriers, samplers, and foldable furniture.