Reflection and transmission properties of a new type of frequency selective surface (FSS) made of zigzag metallic elements placed periodically on a dielectric substrate are investigated theoretically for arbitrary polarisation. The electric field integral equation technique with the subdomain overlapping piecewise sinusoidal basis functions are employed to compute the unknown current coefficients induced on the metallic elements. The zigzag FSS arrays act as a low-pass filter in S-(1-5 GHz), X-(8-12 GHz) and K-u-(12-18 GHz) bands. Owing to multiple resonances the zigzag FSS arrays can be used in multiband frequency applications. Between the resonances there exist transmission windows that allow full energy transfer. By removing the first and third arms, the power reflection coefficient of three-arm zigzag FSS is compared with a freestanding strip FSS, and it is compatible with the measured and calculated results found in the literature.