AbstractThis paper considers the related problems of designing distributed parameter model following control systems and distributed parameter state observers. The synthesis of a model following control system consists of choosing a feedback law so that the state of a plant will faith fully follow the state of a reference model. The design of a state observer reversly consists of choosing a feedback law so that the computed output signals of the observer follow the measured output signals of the plant.The physical realization of both the real model following control system and the state observer, demand the implementation of a mathematical model of the real plant, which is preferably achieved by computer simulation. Examples of de signing model following distributed parameter systems and of state observer simulations are given.