Bi-modulus elastic materials are materials possessing different elastic properties in tension and compression. Some cord-reinforced composites display such characteristics under load application. Cord-reinforced rubber composites, in particular, are striking examples of such materials. The behaviour of these composites can be explained by the fact that the reinforcing cords are one-dimensional structural members with high tensile stiffness but no—or very little—resistance to compressive forces, if they are not restrained. These cords, however, show compressive stiffness, if embedded in a matrix due to the elastic support of the matrix. The overall compressive stiffness of such composites may therefore greatly differ from their tensile stiffness, depending on internal cord-matrix geometry as well as their relative stiffnesses. The material properties are therefore stress-dependent in a general case of combined stresses. Consequently one cannot employ the classical elasticity constitutive equations to correctly analyse the response of these composites. The stress-strain relations for general anisotropic bi-modulus materials—as well as for the orthotropic and isotropic classes—were developed and discussed by Tabaddor with references to other similar work. Some physical aspects of the problem, for two-dimensional composites, have been discussed by Tabaddor. In the present work, beams made of orthotropic bi-modulus composites, under the action of lateral loads, are analysed. It is seen that the analysis is far more complicated than that of classical theory. The results of some experiments on wire-reinforced rubber composite beams are presented. The beams were numerically analysed with the aid of the developed formulation and the predicted deformations are compared with experimental results.