Discrete mathematical models of diffraction of monochromatic wave on ideal conductive infinitely thin pre-Cantor bounded grate and periodical multi-element with pre-Cantor set of tapes on a period are built. The approach is based on the developed by one of the authors of a numerical-analytical method, which allows one to reduce all considered diffraction problems to singular integral equation of first order on a system of intervals and its subsequent numerical solution by the method of discrete singularities (MDS).