During the two last decades, topology optimization has grown to be an accepted and used method to produce conceptual designs. Topology optimization is traditionally carried out on a component level, but in this project, the possibility to apply it to airframe design on a full scale aeroplane model is evaluated. The project features a conceptual flying-wing design on which the study is to be carried out. Inertia Relief is used to constrain the aeroplane instead of traditional single point constraints with rigid body motion being suppressed by the application of accelerations instead of traditional forces and moments. The inertia relief method utilized the inertia of the aeroplane to achieve a state of quasi-equilibrium such that static finite element analysis can be carried out. Two load cases are used: a steep pitch-up manoeuvre and a landing scenario. Aerodynamic forces are calculated for the pitch-up load case via an in-house solver, with the pressure being mapped to the finite element mesh via a Matlab-script to account for different mesh sizes. Increased gravitational loads are used in the landing load case to simulate the dynamic loading caused in a real landing scenario, which is unable to be accounted for directly in the topology optimization. It can be concluded that the optimization is unable to account for one of the major design limitations: buckling of the outer skin. Approaches to account for the buckling of the outer skin are introduced and analysed, with a focus on local compression constraints throughout the wing. The compression constraints produce some promising results but are not without major drawbacks and complications. In general, a one-step topology optimization to produce a mature conceptual airframe design is not possible with optimization algorithms today. It may be possible to adopt a multiple-step optimization approach utilizing topology optimization with following size and shape optimization to achieve a design, which could be expanded on in a future project.