The periodic structure based on an array of multiple conducting strips per unit cell on a chiral slab is investigated in this letter. Instead of a single strip, a unit cell is constructed by equal and unequal lengths of double or triple strips. In this case, the array is periodic, as opposed to the traditional individual elements. The co‐polarised reflectance, co‐polarised transmittance and cross‐polarised transmittance of new types of frequency selective surfaces (FSS) comprised of perfectly conducting double or triple strips on a chiral slab are analysed theoretically for a plane wave at normal incidence. The analysis is based on the modal expansions and moment methods together with the Floquet theorem. The unknown current coefficients induced on the conducting elements are computed by using the subdomain overlapping piecewise sinusoidal basis functions. By using two or three conducting strips per unit cell, FSS can be operated in different frequency bands. The double and triple strips per unit cell on chiral slab produce double and triple resonances, respectively. The structure can be used in band‐stop filter, multiband antenna applications and subreflector systems as well as the polarisation rotator. The computed result of free‐standing strip FSS is compatible with the measured and calculated results in literature.