During the course of the preceding decade, numerous solutions to laminated plate problems have appeared in the literature. This has been the direct result of the development of new materials, e.g. Carbon Fibre Reinforced Plastics (CFRP), for the aerospace industry, where lightness allied with stiffness are characteristics of paramount importance. However, it appears that few, if any, solutions have been published for the case of plates on elastic foundations, even though such solutions may be useful when analysing the face behaviour of certain types of foam-filled, sandwich panels. In attempting to provide such solutions and to establish the effect of the foundation on the plate response, the subsequent analysis was undertaken. As a first step towards this goal, it appeared sensible to consider the simple case of a plate strip, before considering the more complex case of a finite plate. Consequently the analysis and results presented herein are restricted to plate strips.