A circumferentially extending brush seal positioned between static and rotary components of a machine and, during operation of the machine, the brush seal having a higher pressure region at an upstream side and a lower pressure region at a downstream side. The brush seal may include a plurality of bristles forming a bristle pack carried by the static component and cantilevered toward the rotary component such that tips of at least some of the bristles engage the rotary component. The brush seal further may include a pressure plate and a bristle pack backing plate. The bristle backing plate may include a plurality of radially extending and circumferentially spaced slots opening through opposite sides thereof. The slots may be disposed on an inner radial edge and an outer radial edge of the bristle backing plate.