The present work is devoted to the generalisation of operator approach for the solving electromagnetic waves diffraction problems by periodic systems of discontinuities (such transverse slot) in hybrid metal-dielectric structures. The diffraction problem solution of single eigenwave of the hybrid metal-dielectric structure by bounded periodical slot sequences in the metal has been presented. The approach based on the using of semi-infinite periodical structures conception. On the first stage the reflection and propagation coefficients of single slot was found. On the second stage the reflection and propagation coefficients of the semi-infinite sequences of identical discontinuities was found. On the third stage the electrodynamical characteristics of the bounded sequence of identical slot discontinuities was found. By the numerical simulation the dependencies |S₁₁| and |S₁₂| of the structure with single slot and bounded sequences arranged equidistantly was founded. The pattern characteristics are presented.