Timoshenko's shear coefficient for flexural vibrations of beams was computed for circular, elliptical, parabolic, and oval cross sections. A formula for the shear coefficient was obtained by calculating the frequency (from the free-vibration equations of Timoshenko) at which an infinite beam vibrates without transverse deflections and by equating this with the frequency calculated from the 3-dimensional equations of small vibrations of an elastic body. Approximate frequencies obtained by Hidaka (Mem. Imp. Marine Observ., Kobe, Japan 4:99-219, 1931) were used for the ovals, but the other frequencies, as calculated from the equations for small vibrations, were exact. The calculated shear coefficients were tabulated, and all were within about 10% of the coefficient for the rectangular section.