The determination of coupled frequencies of free vibration for beams of nonsymmetric, open cross section is discussed in this paper. Beams with various end conditions, including simple supports, fixed ends and a cantilever, are considered. Results of both exact and approximate analyses are presented. For practical use, a simple approximate formula for determining frequencies of vibration for beams with any end conditions is given. The accuracy of the approximate formula is shown by comparison with results obtained by the exact method. The exact calculations were carried out on an IBM 605 Card Programmed Calculator.