A segmented turbine shroud for radially encasing a turbine in a gas turbine engine comprises a carrier comprising a flange; a ceramic matrix composite (CMC) seal segment comprising a portion defining a pin-receiving bore; an elongated pin extending through the pin-receiving bore; a bushing surrounding the elongated pin within the bore; and a flexible mounting member, the flexible mounting member being connected to the bushing and the carrier flange to thereby flexibly mount the CMC seal segment to the carrier.