A combustor assembly includes a first combustion chamber member and a second combustion chamber member. The first and second combustion chamber members are each formed of a CMC material and include adjacently positioned coupling flanges. A mounting assembly includes a pair of mounting flanges positioned on opposite sides of the coupling flanges of first and second combustion chamber members. An attachment member of the mounting assembly clamps the pair of mounting flanges together to mount the first and second combustion chamber members.