INTRODUCTION Background This Item is one of a group of three Data Items concerning the vibration of liquid-filled pipelines. Graphical and computer methods are provided for the estimation of the natural vibration parameters of planar piping systems. Natural vibration data generated by the computer program of this Item can be used@ in conjunction with the methods of Item No. 89030 (Reference 33)@ for the prediction of the fluctuating values of the liquid pressure and flow and the structural response of planar pipelines following disturbances to the flow. The third Item in the group allows similar estimates to be made of these transient response data in more complex systems that are not necessarily planar. A method of analysis is used in the third Item that does not require the separate calculation of the natural vibration parameters.