While there is a large variety of theories for predicting the mechanical behaviour of laminated shear-deformable composite beams the Refined Zigzag Theory (RZT), originally presented by Tessler et al. (2009, 2010) is proven to be one of the most promising approaches. This is due to its simple setup and superior prediction capability. Since its appearance many contributions have been published dealing with finite beam elements for laminated structures based on the efficient kinematics of RZT. Beam models for plates under plane strain conditions are often used at the preliminary design stage avoiding computationally expensive 2D-or 3D-FE computations. When structures are in contact with or embedded completely in soil different foundation models can be applied. Today a good compromise between accuracy and effort lays in the use of a two-parameter foundation model (Scott 1981) for the representation of the elastic half-space. The standard FE procedure is applied, starting from the principle of virtual displacements and using the specific anisoparametric shape functions which guarantee locking-free solutions. Explicit matrices are derived which represent the effect of the subgrade reaction. The results are compared with available solutions.