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The electromagnetic (EM) field's diffraction problem on the finite periodic lattice embedded in the usual dielectric is considered. The element of the lattice represents the conductor wire with small electrical radius and with shape of the Cassini oval. Such structures have interesting resonant properties in wide frequency range. The Method of Auxiliary Sources (MAS) is used to solve this problem. The first part of this paper represents the theoretical background for considered problem. Next are presented some numerical results which we obtained using the computer simulation.