Substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures. The motion of each of the substructures is represented by a series of admissible functions (vectors), and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures. Because the series of admissible functions (vectors) represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions, the computed eigensolution is only an approximation of the actual one. Convergence of computed eigenvalues to actual eigenvalues requires two limiting processes, one in which the number of admissible functions (vectors) is increased and the other in which the number of geometric compatibility conditions is increased.