In a recent paper by Mindlin and Herrmann, a one-dimensional theory of compressional waves in an elastic rod was described. This theory takes into account both radial inertia and radial shear stress and, accordingly, contains two dependent variables instead of the one axial displacement of classical rod theory. The solution of the equations for the case of forced motions thus involves complications not usually encountered. The difficulties may be surmounted in several ways, one of which is presented in this paper. The method described makes use of Lagrange’s equation of motion and reduces the most general problem of forced motion to a free vibration problem and a quadrature.