A system for restraining relative lateral and/or vertical movement between adjacent support tiles of an elevated building surface assembly. The system is usable with a support structure including a plurality of support pedestals that are disposed in spaced-apart relation on a fixed surface and that are disposed beneath corner portions of surface tiles to vertically support and elevate the tiles above the fixed surface. The system includes stability members that may be inserted into predetermined gaps between adjacent surface tiles so as to be fit between adjacent surface tiles to restrict lateral and/or vertical movement of the tiles. Fasteners may be placed through apertures in inner portions of the stability members into the top surface of the support pedestals to further secure the stability members to the support pedestals.