Free vibrations of beams containing split regions are investigated. General solutions for unsplit and split regions are first established. Recurrence equations relating integration constants for adjacent interior regions are established by satisfying continuity conditions at junctions of interior regions. The frequency determinant is then obtained by satisfying continuity conditions at junctions between end regions and interior regions immediately next to the end regions. Numerical examples are presented for illustrative purposes. Some numerical results are compared to results for a lumped mass model and to limited experimental measurements.