This paper deals with the structural modeling of a family of similar, actual structures taking into account uncertainties and modeling errors. Only errors of the “structural stiffness” type are considered. We develop a new theory in which what we call the lack of knowledge (LOK) is defined through an internal variable, whose upper and lower bounds are stochastic, associated with each substructure. Two main questions are discussed: the impact of the basic LOKs on the predicted structural response and the reduction of the basic LOKs through the use of additional information.