A sudden reduction of the fluid flow yields a pressure shock, which travels along the pipeline with a high speed. Due to this transient loading, dynamic hoop stresses are developed, that may cause catastrophic damages in pipeline integrity. The vibration of the pipe wall is affected by the flow parameters as well as by the elastic and damping characteristics of the material. Most of the studies on dynamic response of pipelines (a) neglect the effect of the material damping, and (b) are usually limited to harmonic pressure oscillations. The present work is an attempt to fill the above research gap. To achieve this target, an analytic solution of the governing motion equation of pipelines under moving pressure shock is derived. The proposed methodology takes into account both elastic and damping characteristics of the steel. With the aid of Laplace and Fourier integral transforms and generalized functions properties, the solution is based on the transformation of the dynamic partial differential equation into an algebraic form. Analytical inversion of the transformed dynamic radial deflection variable is achieved, yielding the final solution. The proposed methodology is implemented in an engineering example; and the results are shown and discussed.