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A method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed. The method is applied to two composite microstructures: a two-phase laminate and a fiber composite. The dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good. The dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature. The agreement between the approximate model, the experiments, and the computations is very good in the wave guide case and satisfactory for the wave reflect case.