This paper presents a novel technique for the accurate modeling of printed periodic structures with thick metal patches. These structures include capacitive frequency selective surfaces (FSS) and metallo-dielectric electromagnetic band-gap (EBG) structures, and are typically modeled under the hypothesis of infinitely thin metal patches. Nevertheless, taking into account the finite thickness of the patches allows for a more accurate modeling, especially at mm-wave frequency, as well as for a better evaluation of conductor losses. The analysis technique proposed in this paper is based on the MoM/BI-RME method and permits to obtain an accurate and computationally efficient modeling tool. A validation example is reported in the case of a capacitive FSS and is compared to the results obtained with a commercial full-wave electromagnetic software.