This chapter discusses the requirements, selection and development of a deployable cold hibernated elastic memory (CHEM) foam structure based on the shape memory polyurethane (SMPU) material system to be deployed into Low Earth Orbit (LEO) on board the International Space Station (ISS). Inflatable space structures were first used in the Project Echo passive communications satellite experiments launched in 1960 and 1964. These were metalized balloon satellites acting as passive reflectors of microwave signals. Since then, more complex inflatables have been developed, such as International Latex Corporation (ILC) Dover’s Inflatable Re-entry Vehicle Experiment (IRVE) for NASA. Over the past few decades, shape memory alloys (SMAs) have been utilized in many fields, including aerospace engineering (e.g., actuators in deployable structures and morphing wings) and medical devices, though most shape memory effect (SME)-based components are small. The advantages of SMPUs over SMAs and SMPs are the low material density and the much higher deformability and recovery rates of the cellular structure.