A turbine engine shroud segment is provided with a radially outer surface including a pair of spaced apart, opposed first and second edge portion surface depressions, for example spaced circumferentially, having a seal surface shaped to receive, in a surface depression formed between assembled adjacent segments in a shroud assembly, or axially assembled adjacent segments and engine members, a radially outer fluid seal member. The depression portions of a shroud segment are joined with the radially outer surface of the shroud segment through an arcuate transition surface. Stresses generated during engine operation in the shroud material are reduced, enabling practical use of a low ductility material, for example a ceramic matrix composite. The edge portion surface depressions are provided with a first shape and the fluid seal member, disposed at the depression, is provided with a surface of a second shape matched in shape with the first shape.