In this work, we present a study on the effects of modifications on wing geometric configurations via morphing. Specifically, we investigate the resulting impacts on aeroelastic stability. In the primary analysis presented, we assess a wall-mounted configuration for an airfoil section of a two-dimensional wing. This morphing-wing system comprises a torsional spring at the trailing-edge flap hinge, which induces the morphing phenomenon. The behavior of this system is studied within the context of divergence and reversal. The analysis following this examines a highly flexible flying-wing configuration, subject to a transient morphing scheme. The geometries corresponding to the unmorphed and morphed configurations are acquired from a physical morphing trailing-edge wing prototype, and the structural modeling and cross-sectional properties are obtained using the Gmsh tool and variational asymptotic beam sectional analysis. Furthermore, we evaluate the effects of the geometric variations on the aeroelastic stability through leveraging the computer program, NATASHA (which stands for nonlinear aeroelastic trim and stability analysis of high-altitude long-endurance aircraft). The results obtained from this analysis insinuate the favorable impact on the aeroelastic stability of the system, namely, in terms of flutter characteristics.