An elastic energy method is presented for finding the fundamental torsional vibration frequency of solid rectangular beams without boundary constraints. A Rayleigh‐Ritz method is employed, and the results, which were calculated on an IBM 650 computer, are shown. Also illustrated is the effect a change in the Poisson's ratio of the beam material has on the fundamental frequency. A comparison is made with results of torsional vibration tests performed at the National Bureau of Standards. This comparison indicates that the analytical method employed gives fairly accurate results.