A method of analysis is presented for determining the dynamic response of bridges supported on long piles extending through deep sensitive clays, when the bas of the clay medium is subjected to a seismic disturbance. The study is separated into two parts: (1) The dynamic response of the clay medium alone; and (2) the determination of the interaction of the entire structural system, including the piles, with the moving clay medium. The formulation of the second part of the analysis involves discrete parameters that characterize the elastic, inertia, creep, and damping properties of the clay medium. A procedure is developed that provides a simple means by which these dynamic parameters can be evaluated. Nonlinear aspects of soil properties are included in the evaluation of coefficients. Using this proposed method of analysis, an approximate solution sufficiently accurate for design purposes can be obtained on a digital computer using step-by-step methods of analysis. Some preliminary results of the application of this method to the study of a typical bridge are presented in graphical form.