A flexible coupling assembly for connecting two shafts in a coaxial alignment has a flange including a hub with axially opposite first and second ends and a plurality of radial grooves angularly spaced about a periphery of the hub. The radial grooves have crests and roots. The radial grooves extend axially along a length of the hub and are shaped in a manner such that a diameter of the crests at a position on the hub adjacent to the first axial end of the hub is greater than a diameter of the crests at a position of the hub adjacent to the second axial end. The coupling includes a flexible insert comprising a resilient member having an inner surface and an outer surface. The flexible insert inner surface has a plurality of notches adapted to cooperate with the flange hub radial grooves.