Equations are derived for description of the stress-deformed state of a two-layer perforated plate, the lower layer of which represents itself a system of rectilinear ribs. A calculation is carried out of displacements of a two-layer circular plate of a plane-convex mirror of a telescope. The plate is under action of the dead weight and leans on three points situated on a circle at equal distance one from the other. The optimal radius of the circle is determined which corresponds the minimum value of the mean-square deflection of the telescope mirror. The dependence of the deflection on the circle radius is presented.