This paper presents a parametric study of square loop and square slot frequency selective surfaces (FSS) aimed at their equivalent circuit (EC) model optimization. Consideration was given to their physical attributes, i.e. the unit cell dimensions and spacing, substrate thickness and dielectric properties, for several frequencies and plane wave incident angles. Correlation analysis and evaluation of the influence of physical related input parameters on the FSS performance, is presented. Subsequent optimization factor for the square loop classical EC model is analyzed, and a novel EC model formulation for the square slot FSS, is proposed. The performance of the proposed EC model was assessed against results obtained from appropriate electromagnetic (EM) simulations, based on a root-mean-square error (RMSE) criteria. Results demonstrate the validity of the optimized EC model, in which good estimations of the frequency response of FSS structures were obtained. Significant reduction of the resonant frequency offsets, in the order of 650 (from 910 to 260) and 460 (770 to 310) MHz, were obtained for square loops and square slots, respectively. The models were further validated against measurements performed on two physical FSS prototypes inside an anechoic chamber, at 2.4 GHz. Relatively good agreement was obtained between measurements of real FSS prototypes and results obtained with the EC model. Finally, this work is sought to provide the necessary refinement of elementary models for further studies with more complex and novel FSS structures.