A shroud apparatus for a gas turbine engine, comprising: a shroud segment comprising a ceramic matrix composite material and having a cross-sectional shape defined by opposed forward and aft walls (124, 126), and opposed inner and outer walls (120, 122), the walls extending bet ween opposed first and second end faces, wherein the inner wall defines an arcuate inner flowpath surface, wherein the shroud segment includes: a radially-inward facing chordal forward mounting surface defined by the outer wall extending axially past the forward wall to define a forward flange; and a radially-inward facing chordal aft mounting surface defined by the outer wall extending axially past the aft wall to define an aft flange; and an annular case surrounding the shroud segment, the case including: a radially-outward facing chordal forward bearing surface which engages the forward mounting surface; and a radially-outward facing chordal aft bearing surface which engages the aft mounting surface of the shroud segment; wherein the outer wall has a shorter axial length than the inner wall, and each of the forward and aft walls (124, 126) extend away from the inner wall at an acute angle. a shroud segment comprising a ceramic matrix composite material and having a cross-sectional shape defined by opposed forward and aft walls (124, 126), and opposed inner and outer walls (120, 122), the walls extending bet ween opposed first and second end faces, wherein the inner wall defines an arcuate inner flowpath surface, wherein the shroud segment includes: a radially-inward facing chordal forward mounting surface defined by the outer wall extending axially past the forward wall to define a forward flange; and a radially-inward facing chordal aft mounting surface defined by the outer wall extending axially past the aft wall to define an aft flange; and an annular case surrounding the shroud segment, the case including: a radially-outward facing chordal forward bearing surface which engages the forward mounting surface; and a radially-outward facing chordal aft bearing surface which engages the aft mounting surface of the shroud segment; wherein the outer wall has a shorter axial length than the inner wall, and each of the forward and aft walls (124, 126) extend away from the inner wall at an acute angle. a radially-inward facing chordal forward mounting surface defined by the outer wall extending axially past the forward wall to define a forward flange; and a radially-inward facing chordal aft mounting surface defined by the outer wall extending axially past the aft wall to define an aft flange; and an annular case surrounding the shroud segment, the case including: a radially-outward facing chordal forward bearing surface which engages the forward mounting surface; and a radially-outward facing chordal aft bearing surface which engages the aft mounting surface of the shroud segment; wherein the outer wall has a shorter axial length than the inner wall, and each of the forward and aft walls (124, 126) extend away from the inner wall at an acute angle. a radially-outward facing chordal forward bearing surface which engages the forward mounting surface; and a radially-outward facing chordal aft bearing surface which engages the aft mounting surface of the shroud segment; wherein the outer wall has a shorter axial length than the inner wall, and each of the forward and aft walls (124, 126) extend away from the inner wall at an acute angle.