Reliability is defined as the probability of a system successfully maintaining its function within the specified time under the specified condition. Reliability theory has been mainly developed for single-function system with single reliability structure of the system [1–2]. Its theory has been extended to the systems with multiple component states [3–7] and some latest study and review can be seen in [8–9]. Nowadays, more and more products are designed to be multi-functional or provide multiple features to the customers. If all functions are equally important and required to function all the time, this can be treated same as a single-function system in reliability modeling and analysis. However, many multi-function systems cannot be treated this way. In those cases, the system reliability of single function or the combination of the functions may need to be modeled and analyzed individually as well as collectively. In this paper, a variety of structures of multi-function systems are defined. It shows many definitions and theorems of single-function system can be extended to multi-function system. The calculation of multi-function system reliability is discussed and component reliability importance is defined. A numerical example is given to illustrate the methodology.