A sealing gasket assembly includes one or more carriers each having an offset flexible stopper portion spaced laterally outwardly away from an offset inner sealing portion that is adjacent an opening or other area requiring sealing between mating members adapted to be clamped together. An optional shim can be disposed adjacent to, and aligned with, the carrier. A resilient sealing material is applied to at least portions of the carrier and/or the shim, such as by screen printing, for example. The gasket assembly can be used advantageously in sealing applications such as those for cylinder heads and blocks, intake or exhaust manifolds, piping or other fluid conveying devices, housings, enclosures, or other situations where relative movement can occur between the members to be sealed to each other.