The reflection of linearly polarized light from an N-layer system of nanometer-size anisotropic insulating films is investigated. The approximate expressions for reflection characteristics are derived. All analytical results are supported by computeraided analysis made on the basis of general wave propagation theory for anisotropic layered media. It is show that the accuracy of the long-wavelength approximation for nanoscopic anisotropic layered systems is quite satisfactory: if the thickness of a multilayer divided by the wavelength comprises only a few hundredths, then the error of approximate expressions will be of the order of several percent. The most useful feature of obtained formulas is that they are simply invertible, allowing a direct calculation of the parameters of nanoscale layers.