The transmission and reflection properties of frequency-selective surfaces (FSSs) are evaluated through a simple and accurate first-order circuit approach. The approximate analysis, based on the parallel between real structure and a lumped-LC-network counterpart, is also useful for acquiring physical insights into the working principles of frequency-selective surfaces. The first part of the paper describes a technique for computing lumped parameters of the most common frequency-selective-surface elements. The L and C parameters representing a given frequency-selective-surface element are derived only one time, at normal incidence, and stored, so as to form a database. The second part of the paper deals with the derivation of simple relations allowing the generalization of the stored LC couples in the case where the frequency-selective surface is printed or embedded in arbitrarily thick dielectric slabs, when the incident angle is varied from normal incidence, or if a different periodicity with respect to the reference periodicity is adopted. The generalized lumped parameters are included in an equivalent transmission line for computing the response of generic frequency-selective-surface configurations with no additional computational effort. The results obtained through the simplified model presented here are verified by a careful comparison with MoM simulations.