Several technologies and tools have been proposed to assist rehabilitation team in performing exercises. They can help rehabilitation specialists to manage more patients when practicing their exercises, either in presence or remotely. They also make it possible to support patients to do parts of the program at home. Few contributions deal with supporting to the engineering of training platforms for post-stroke rehabilitation. Designers and developers of training platforms for post-stroke rehabilitation do not have a conceptual framework to rely on to develop training Hardware (HW)/Software (SW) platforms. Furthermore, the development and implementation of training platforms for post-stroke rehabilitation requires being able to engineer training platforms with multiple HW and SW components and to engineer coordinated and relevant connections between these components. This paper describes the MUMR (Multi User Multi Role)-MIODMIT technique to design the architecture of the interactive systems for post-stroke rehabilitation training. This technique is based on the MIODMIT description technique for the architecture of interactive systems and enables to describe the main aspects of a post-stroke rehabilitation training platform. The proposed technique is applied to two examples of rehabilitation training platforms.