The dynamic behaviour of frame structures is greatly influenced by the presence of concentrated damage, both in linear and non-linear context. Namely, the presence of cracks determines a modification in the linear dynamic properties and, furthermore, can produce a significant reduction on both the resistance and ductility of the structures. This work deals with beam-like structures in presence of cracks and introduces a novel beam element with discontinuities that is adopted for a FEM discretisation. The aim of the work is evaluating the influence of multiple cracks on the linear dynamic properties of frame structures. The presented results constitute the basis for a non-trivial extension to the non-linear static and dynamic context