We derived a traveling wave form of the exact solution using a single equivalent propagating wave, an extension of the classical d’Alembert formula to finite length structures with boundary damping. We considered nonzero initial displacement at the ends. In the literature, the associated discontinuity is avoided by restricting the initial displacement to be zero at the ends. We found that for nonzero end displacement there exists an additional, piecewise constant term, which we denoted by ‘‘end waves’’, that is essential to keep the response continuous.