This book is a compendium of knowledge on the finite element method (FEM) applied to beam and plate structures resting on elastic foundation. Providing a theoretical description of beam and plate elements and elastic foundations, we use the displacement approach to the FEM. Such description serves as a basis for creating software for elastic-plastic analysis of structures resting on elastic foundation. Making use of the FEM, we have created a program written in the Fortran language for solutions to problems of placing structural elements on elastic foundation. A structure can be discretized by means of isoparametric beam finite elements, and isoparametric Lagrangian Mindlin plate finite elements. We describe a foundation with special isoparametric finite elements. The software allows the user to model layered structures of any form, accounting for elastic-plastic material properties, i.e. physical non-linearity, of beam and plate elements resting on non-homogeneous foundation: three-parameter foundation under beam elements, two-parameter – under plate elements, accounting for the outside of the beam, foundation layers and unilateral conditions in structure-foundation interaction.