This paper presents a new method for predicting vibration characteristics of a structure that is considered to undergo a design change. It is assumed that for the original structure the vibration data are available either as a complete or as an incomplete set. On the basis of the available vibration data and the known data on the design change, this paper discusses methodologies for determining the vibration characteristics of the modified structure. By considering practical situations, the emphasis of this paper is on structures for which a finite element model, and hence a stiffness matrix, is not available. If a finite element model of the structure is already available, then predicting the modal characteristics of the modified or redesigned structure may be a trivial task. However, if a finite element model of the structure is not available, then a more economical procedure would be to predict the vibration characteristics of the modified structure from experimentally obtained vibration data. Here the idea is to use the available vibration data and to combine them with the structural data of the proposed design change, in order to predict the vibration characteristics of the modified structure. When the vibration data for a structure are obtained experimentally, probably only a limited number of mode shapes and their corresponding natural frequencies can be computed (an incomplete set of modal data). This paper presents the necessary formulations for both complete and incomplete mode sets. Although the main portion of the paper concentrates on identifying the structural stiffness matrix, a methodology is also presented for mass matrix identification. For validating the developed formulations, two examples with numerical results are presented.