The intensive design optimization process of airframes has the effect of decreasing the structural stiffness, inducing large deformations that can have significant effects on the flight loads and the trimming configuration of aircraft. Such changes in the dynamic response of airframes are captured by considerations of geometric nonlinearity effects in the formulation of the aeroelastic solutions. In this thesis, a number of methodologies to model structural geometric nonlinearity, ranging in complexity, are studied at length to assess their effectiveness and accuracy in aeroelasticity simulations. The adopted methodologies are also benchmarked against wellestablished commercial Finite Element Method (FEM) solution sequences, namely, MSC Nastran and ASWING.