In this paper it is shown how the branches of Pochhammer’s frequency equation for flexural waves in a circular cylinder may be constructed approximately with the aid of a grid of simpler curves and asymptotic equations for long and short wave lengths. With very little computation, in comparison with that required in the direct determination of the roots of Pochhammer’s equation, a qualitative view is obtained of the relations between frequency, phase velocity, group velocity, and propagation constant, for any branch, as well as some information as to the shapes of the modes.