In practice, fibrous and layered composite beams have periodically and locally curved layers because of the design considerations and manufacturing processes. In this study, the effect of these curvatures and composite material properties to the natural frequencies of the beams is investigated. The periodically curved layered composite material of the considered beam is modelled with the use of the continuum theory proposed by Akbarov and Guz. The free vibration problems are solved by employing the finite element method. Obtained natural frequencies of the beams are presented for the different parameters of the curvature, modulus of elasticity and support condition of the beams. For the case that the ratio of the modulus of elasticity of the layers equals to one and the parameter of the curvature equals to zero, the results converge to natural frequencies of a classical Euler-Bernoulli beam. Results are in good agreement with the literature.