Aero-structural optimization is a keystone to concurrently improve aerodynamic performance and reduce the structural mass of an aircraft. Gradient-based multi-disciplinary design optimization is actually efficient if gradients computations are fast and accurate enough. This paper presents two high-fidelity aero-structure gradient computation techniques for design variables impacting the stiffness of the structure. A first part details the new module developed and implemented in the Onera elsA software capable of computing aero-structure gradients using intrusive direct and adjoint methods. In a second part an alternative improved uncoupled non-intrusive approach is proposed. Both approaches are evaluated and compared on the Common Research Model (CRM) test-case considering criteria such as accuracy, efficiency, and applicability on practical industrial problem. Finally, preliminary results are presented on an inverse design problem. The final objective will be to match a target twist distribution on the Common Research Model wing using this new coupled gradient capability.