This paper considers the response of a semiinfinite viscoelastic rod subject to an enforced sinusoidal displacement of its end. The rod has external elastic constraint along its length. Above a certain critical frequency, the steady‐state solution consists of damped traveling waves moving away from the forced end. For lower frequencies, however, the wave travels out of the rod toward the forced end. A brief explanation of this interesting phenomenon is given by studying the work done on the rod. The transient analysis is performed, for the rod initially at rest, by applying a Fourier sine transform to the space variable. The resulting integral solution is integrated numerically for a purely viscous rod being forced at a frequency below the critical frequency. This solution shows how the disturbance is initially propagated away from the forced end and subsequently settles down to the steady‐state solution of the wave traveling toward the forced end.