A seal member for effecting a seal preventing fluid flow in an axial direction through an annular space formed between two relatively moving components including a rotatable shaft and a stator structure. The seal member includes a plurality of flexible seal strips. Each seal strip includes a planar plate extending radially through the annular space and having a radially outer end supported to the stator structure and a radially inner end defining a tip portion extending widthwise in the axial direction engaged in sliding contact with a peripheral surface of the rotatable shaft. At least one of the seal strips includes a plurality of perforations extending through the seal strip and located between a leading edge and a trailing edge of the seal strip for effecting an increased flexibility of the seal strip adjacent to the tip portion.