Abstract: Based on a mathematical model that describes the three-dimensional response of the axially moving cable with small sag and on the concept of wave propagation, an exact solution for the linear, in plane transverse vibration of the axially moving cable with general boundary conditions is obtained. The expression of the solution is derived in frequency domain and interpreted in terms of wave propagation functions. The physical interpretations of the vibrational response will play an important role in the design of active vibration wave controllers. The axially moving cable with fixed boundary conditions in two ends is used as an example to investigate the effect of equilibrium curvature on the dynamic responses and wave propagation.