The purpose of this study was to develop a theoretical means for predicting the longitudinal motion of computer tape in a high-performance tape drive. In particular, this paper treats the motion that is governed by traveling velocity-stress wave reflections, attenuations, and interactions in the length of tape between the tangency point at the capstan and the tangency point at the stubby column in the drive. The motion of the tape was determined by solving the classical, damped, one-dimensional wave equation subject to the appropriate boundary conditions. J. C. Snowdon's low-damping constitutive model was used to describe the viscoelastic behavior of the tape. The solutions for simple boundary conditions were experimentally verified by mechanical impedance techniques. More complex boundary conditions, such as those for vacuum columns, were experimentally studied to determine the true mathematical boundary conditions. This paper also discusses simple unreflected harmonic waves, simple reflected harmonic waves, and general periodic reflected waves as examples. The significance of the wave interactions in the design of tape drives is considered.