Electromagnetic bandgap (EBG) structures are used to suppress surface wave (SW) propagation in printed antenna systems. Although there are several different types of EBG structures, not all of them can be utilized in flexible applications. As a promising flexible EBG structure, perforated high impedance surfaces (PHIS), which also behave as artificial magnetic conductors, were previously reported. However, due to the asymmetry of their geometry, they can suppress SW in only one direction. This paper reports a symmetrical PHIS, which suppresses surface waves in more than one direction. The geometry of the perforations and patches are optimized to overlap the reflection phase and SW suppression bands.