An elastic theory for Langmuir-Blodgett films is presented. The expression for the free energy density of the film is obtained in terms of the deformation tensor by means of symmetry considerations and by making use of a quasi-microscopic model. The influence of a linear term in the deformation tensor in the elastic energy density is analysed. It is shown that when the elastic constant of the linear term is larger than a critical value, the ground state of the film is periodically distorted.