[en] The exact solution of the static equilibrium problem of an isotropic film in the linear elastic theory is studied for arbitrary thickness and for arbitrary boundary condition. From the symmetry principle, the solution is simplified into an invariant form with several scalar functions to be determined. The equilibrium solution is presented explicitly in the wave-vector space and given in the form of an integral expression in real space. An approximated equilibrium solution in real space is proposed, and the equilibrium of the plate as a thin film is discussed briefly.