This paper proposes a new frequency selective surface (FSS) based on the combination of four sinusoidal-waveform like shapes, each formed by the combination of two semi-circles, for an overall arrangement similar to a square shape. The proposed design was simulated and evaluated through a commercial electromagnetic (EM) simulation software. The sine-square FSS has a relatively simple design, yet provides a dual band frequency response, with narrow bandwidths compared to classical designs, and with a relatively stable angular behavior of up to at least 45 • . It was shown that the second resonance frequency can, within a limited range, be independently controlled from the first resonance frequency band. Both band reject and band pass variants, as well as possible active/tunable implementations of this FSS design, were evaluated and are discussed in this paper.