A seal member for effecting a seal preventing fluid flow in an axial direction through an annular space formed between a rotatable shaft and a stator structure. The seal member includes a plurality of flexible seal strips 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 for engaging in sliding contact with a peripheral surface of the rotatable shaft. The seal strips are mounted to the stator structure with the tip portions of the seal strips at an angle to the axial direction. Each of the tip portions are formed with a curvature in a radially extending plane between a leading edge and a trailing edge of each seal strip.