This paper presents a one-degree-of-freedom network of Bennett linkages which can be deployed to approximate a cylindrical surface. The geometry of the unit mechanism is parameterized and its position kinematics is solved. The influence of the geometric parameters on the deployed shape is examined. Further kinematic analysis isolates those Bennett geometries for which a cylindrical network can be constructed. The procedure for connecting the unit mechanisms in a deployable cylinder is described in detail and used to gain insight into, and formulate some general guidelines for, the design of linkage networks which unfold as curved surfaces. Case studies of deployable structures in the shape of circular and elliptical cylinders are presented. Modeling and simulation validate the proposed approach.