A near flow path seal member for a turbomachine includes a seal body having a seal support member including a first end portion that extends to a second end portion through an intermediate portion. An arm member extends from the first end portion of the seal body. The arm member has a first end that extends to a second end to define an axial dimension of the arm member, a first edge that extends to a second, opposing edge to define a circumferential dimension of the arm member, and a surface having a profile that establishes a thickness variation of the arm member in each of the axial dimension and the circumferential dimension.