Inflatable devices have been used in various applications due to their low cost, light weight, simplicity, and ability to compactly stow yet deploy to large sizes with complex shape. Recently, soft robotics has added active shape change to inflatables’ otherwise static functionality. However, the required complex multi-chamber structures and active pressure control sacrifice many inherent advantages including simplicity and stowability. Many applications require only passive shape change (posability), where users manipulate a device manually, and the device simply holds its new posed shape. This paper explores a new approach using internal string-like tensile elements to provide posability while maintaining stowability and other inherent advantages of inflatables, leveraging concepts in the field of tensegrity mechanisms. Tensegrity constrained inflatables provide posable motion by allowing internal tensile strings to thread through loops as the shape is changed, where friction between the strings and loops retain the new pose. Graphical instantaneous center kinematic analysis techniques for traditional linkage systems are extended to include threaded tensegrity mechanisms, enabling analysis and design of complex posable tensegrity structures. A simple example prototype implementing bending with 1 DOF, demonstrates posable behavior, quantified in terms of the force required to change pose at different angles and pressures. The resulting bistable behavior is explained using the IC kinematic analysis. The kinematic techniques are also applied to the design of one degree of freedom functional building blocks which combine to create tensegrity configurations providing 2 DOF posability in two and three dimensions which are demonstrated through multiple hardware prototypes. The novel technology and design methods presented in this paper provide a foundation for the development of a class of new user-interactive inflatable devices with posable functionality and deploy and stow capability.