This paper presents a computational method for a confidence region of identified parameters which are affected by measurement noise and error contained in prescribed parameters. The method is based on sensitivities of the identified parameters with respect to model parameter error and measurement noise along with the law of error propagation. By conducting numerical experiments on simple models, it is confirmed that the confidence region coincides well with the results of numerical experiments. Furthermore, the optimum arrangement of sensor locations is evaluated when uncertainty exists in prescribed parameters, based on the concept that square sum of coefficients of variations of identified results attains minimum. Good agreement of the theoretical results with those of numerical simulation confirmed validity of the theory.