The dynamic response of buried pipelines to earthquakes is best expressed in terms of dynamic amplification factors, i.e. as the ratio of dynamic to static response. In the present paper, the system is represented by a model consisting of a cylindrical rod of radius a embedded in an elastic medium. The required interacting static response of rods subjected to periodic longitudinal forces at intervals L and acting in alternate directions, is obtained. Such a load pattern corresponds to the incoherent motion occuring in earthquakes. The static displacements and interacting stresses of the system are established and are found to be dependent, for a given medium, on the ratio of stiffness of the medium and rod as well as on the aspect ratio a L. Numerical results are presented for a series of rods governed by the above non-dimensional parameters.