Abstract <p>The paper considers a model of composite plate consisting of single-layer fiber composite. The layers are considered to be a transversely isotropic material with given directions of reinforcement and different elastic moduli in tension and compression. The model is based on the generalized rheological method, and constitutive equations with a potential representation were obtained. The elastic energy functional was obtained using Lagrange’s variational principle. Numerical calculations were carried out using the finite element method with the initial stress method. Using the Lagrange multiplier method, the contact problem of influencing a plate with a rigid stamp is solved. Examples of calculations of bending plates under the action of concentrated forces and a rigid stamp are presented.</p>