Periodic longitudinal vibrations of a video and audio tape and the like used for transducing pictures and sounds may be induced by self-excited vibrations which are caused by frictions against the heads and guides, and their eccentricity, noncircularity or irregularity. It is important to analyze the longitudinal vibration of a tape because it causes distortions of a reproduced signal. It is difficult to measure directly the longitudinal vibration. In this paper a method estimating longitudinal vibration using impulse responses in the transverse direction is presented. And, the parameters boundary domain where the transverse and longitudinal vibration can be decoupled is introduced. In the domain where the both vibrations are decoupled, analytic methods using frequency characteristics and transient responses of the transverse vibration, respectively, are presented. The time domain method predicted more exactly the instantaneous phase of the longitudinal vibration than frequency domain method did.