Abstract: Continuous, discontionuous, continuous—discontionuous medium mechanics models adopted in structural stress analysis are introduced systematically. Various theories and numerical methods in the three models which represent the mainstream and direction of stress analysis nowadays are discussed. With the adventof tall, large-scale, precise and new structures, research effort is still needed in the developmentof the three models. This paper describes the state of the artof stress analysis of continuous-discontinuous structures. It covers a great variety of issues including concepts, continuity to non-continuity, exact and approximate solutions and soforth.