This paper presents a refined finite element analysis for the analysis of two-dimensional plane stress and plane strain structures with particular emphasis being placed on the ability to solve problems of soil-structure interaction under earthquake loadings. The structure and
the soil are idealized as an assemblage of quadrilateral plane stress and plane strain elements having a cubic variation in displacement enabling a more accurate representation of the stiffness properties of the system than that previously available. The response of the system to the earthquake acceleration history is achieved by a superposition of normal mode responses and the methods of obtaining the mode shapes and frequencies are outlined. Examples are presented to illustrate the capability of this approach.