We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of quantum machine learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential of QML in tackling complex classification and regression tasks. Our results showcase the ability of hybrid quantum tensor networks to achieve high accuracy in binary classification and promising performance in regressing discrete variables. While hyperparameter selection remains a challenge, this work contributes significantly to the development of QML for solving intricate problems in aeroelasticity.