A theoretical investigation of infinitely periodic quasi-optical grill structures for excitation of lower-hybrid waves in toroidal plasmas has been undertaken for cylinder grill elements with an arbitrary cross section. The basis for investigation is the expansion of the scattered RF field into the infinite series of spatial harmonics which makes it possible to obtain the integral equation for the distribution of magnetic current over the surface of grill elements and to calculate the efficiency of LH wave excitation depending upon the LH wave slowing-down and parameters of the grill structure and of the plasma layer. The numerical simulation performed for the single-layer grill, with elements of elliptical cross section irradiated from vacuum by infinite plane waves, demonstrates the possibility of achieving a high efficiency of up to 25 - 30% of the unidirectional LH wave excitation with the slowing-down , which is relevant to large fusion installations. The calculations have also been performed for the grill structure irradiated by quasi-optical RF beams with finite cross section; it is shown that the coupling efficiency degrades insignificantly if the RF beam aperture (which may be of the order of the size of the RF port in the direction of the toroidal magnetic field) essentially exceeds the vacuum wavelength of radiation. The results obtained seem to be encouraging for construction of a double-layer grill with high efficiency close to unity and low Q-value of the quasi-optical cavity, resulting in a comparatively low value of RF field intensity near the grill elements and in a weak dependence of grill efficiency upon plasma parameters.