The flexure mount system is disclosed that can accommodate thermal expansion. The flexure mount can include a base, a first flexure mount coupled to the base, a second flexure mount coupled to the base, and a supported structure coupled to the first and second flexure mounts along an axis. The first flexure mount can have a first radial flexure. The second flexure mount can have a second radial flexure and an axial flexure. The first and second radial flexures can be operable to provide radial compliance relative to the axis and the axial flexure can be operable to provide axial compliance parallel to the axis, such that the first flexure mount is radially compliant, and the second flexure mount is radially and axially compliant.