An approximate one‐dimensional theory is developed for axially symmetric torsional deformation of elastic circular composite cylinders. The cylinders are composed of a core perfectly bonded to an outer casing. The equations of motion accommodate the first two frequency branches of the dispersion relation for symmetric torsional waves propagating along the axis of the cylinder. Important parameters are the ratios of densities, shear moduli, and radii of the core and casing. Dispersion relations obtained from this approximate theory are studied for ranges of values of these parameters, and a comparison made with the results of the “exact” theory, i.e., three‐dimensional elasticity. In order to match closely the results from the exact analysis, two correction factors are introduced, and values are tabulated for typical material and geometric properties. Sufficient conditions at the ends of finite cylinders are obtained to provide a unique solution.