The paper develops a finite element scheme for computing the eigensystem for a cracked beam for different degrees of closure. Previous work in the authors' laboratories has indicated that the ability to extend the use of mode superposition to model breathing conditions in the crack zone would overcome the need to switch from a frequency-domain-based model to a time-stepping scheme which had caused both implementational and theoretical problems. In this study, the finite element method, the component mode synthesis method and the linear elastic fracture mechanics theory are integrated for modelling of the cracked structures. It is believed that this is a novel synthesis of methods. The method used by the authors is benchmarked against earlier results in the literature.