This paper is concerned with the free vibration behaviour of elastic beams having hexagonal cellular geometry. The natural frequencies and the mode shapes of the cellular beams are obtained using the finite element method. These values are compared with the theoretically obtained values on the basis of the assumptions that (i) the macroscopic structure behaves as a continuum for low-frequency dynamics, and (ii) the dominant mechanism of deformation is the macroscopic extension and compression. A method for calculating approximate fundamental frequency using static deflection shape is presented. The results obtained by this method axe promising.