Abstract: An apparatus for sealing a flow control apparatus, such as a guillotine damper, is disclosed. The apparatus of the invention is particularly intended for dampers or other flow control devices utilizing pressurized sealing air to effect complete sealing. The closure member is of the type that moves completely out of the main fluid passageway when opened. Each of the two lateral seals, which cooperate with lateral edges of the closure member, includes an extended portion with a curved segment which takes the form of a cylindrical arc to stiffen each lateral seal against movement normal to the plane of the seal. This, in turn, allows considerable reduction in the clearances and gaps in the corners between the lateral seals and an entry seal to reduce the flow volume of the sealing air, to reduce the overall power requirements, and to reduce energy consumption.