The spectral response of the periodic antenna structure placed in a dielectric homogeneous medium depends on the antenna geometry, the parameters of the medium, the angle of incidence, polarization, and the geometry of the excitation field. Increasing the number of antenna structure parameters can be achieved by introducing a multilayer dielectric medium with a certain number of metallized periodic surfaces located on flat boundaries between the dielectric layers. There are two complementary approaches to the analysis of such structures. In the first, the composite antenna system is analysed by constructing supermodes of the entire structure. In the second, the system is considered as a cascade assembly of flat discrete elements, i.e., the boundaries between two dielectrics, periodic metallized planes, and dielectric layers. The latter approach leads to the definition of the scattering, transmission, or impedance matrix of the entire structure by cascading the corresponding matrices associated with the individual discrete elements of the antenna structure. It is particularly useful in modelling dielectric multilayer antenna walls, where the stored data on one planar antenna element can be used many times in the analysis of various antenna systems with modified parameters of other discrete structure elements. Microstrip antennas combine field and peripheral problems and require the use of analytical methods of a high degree of complexity. Therefore, at present, there are no standard methods that can be used in engineering practice. This work is a step towards filling these gaps.