The resonance spectrum of composite plates made of alternating piezoelectric ceramic and epoxy elements is studied both theoretically and experimentally in the frequency range below the thickness resonance. The transmissivity of the finite structure to plate modes is calculated, taking into account the effective plate velocities of the two constituent materials and the finite number of elements in the structure. The results are in excellent agreement with the electrically excited acoustical resonances of samples with different geometry and number of elements. In particular, the effects of the finite size on the number and frequency of modes, as well as their selection rules in the given experimental setup, are successfully interpreted. New ‘‘surface’’ resonances, attributed to the end elements, are observed in the stopbands when the surface elements have lower impedance.