Cross-linked Tetronic star block copolymer gels, based on poly(ethylene oxide) and poly(propylene oxide), behave quite regular with respect to mechanical properties, but exhibits unusual absence of structural response to strain. The elastic response is linear up to more than 100% strain, with a steady-state modulus of the order of 0.01 MPa after an initial stress relaxation. Neutron and X-ray scattering experiments show a consistent but unexpected response to uniaxial strain, with no changes in characteristic molecular dimensions. Upon strain beyond about 100%, that is, when the stress-strain curve is no longer linear, structural texture appears and becomes even more pronounced upon further strain, thus, indicating alignment of the self-assembled hexagonally ordered cylindrical micelles with the cylinder-axis perpendicular to the strain. It is proposed that the main structural response to large-amplitude strain is related to a layer-dominated structure of cross-linked star molecules.