This paper explores the contribution of systems modeling to the design and analysis of viability in service systems. We apply a modeling framework called SEAM (Systemic Enterprise Architecture Method) to gain an understanding of how a service system maintains its identity and remains viable in its environment. SEAM embodies theoretical insights from systems science and organizational cybernetics, in particular the viable system model of Stafford Beer. We illustrate the applicability of the framework by modeling the design of viability in a service system.