With the need to drastically reduce aircraft emissions and fuel burn, there have been significant strides towards the design of fuel-efficient aircraft. This has involved moving towards extremely high aspect-ratio wings that need to be aeroelastically tailored and unconventional aircraft configurations. However aeroelastic stability of such configurations is a major challenge. In order to ensure that the fuel-burn improvements predicted in the conceptual or early preliminary design phase are attained in reality, it is essential to ensure that aeroelastic constraints are enforced early on in the design phase itself. However inexpensive yet accurate computation of transonic aeroelasticity especially transonic flutter predictions is quite a challenge due to the non-linearity in the flow at transonic regimes which requires non-linear fluid dynamics approaches that are generally too expensive for the early design phases. In this work we attempt to address this issue by first developing a two-dimensional parametric transonic low-order model that accurately predicts unsteady flow results for airfoils. A set of airfoil agnostic parameters for this model are obtained that permit accurate two-dimensional transonic aeroelastic simulations. This approach is then extended into three dimensions using the ASWING Weissinger model formulation. Next a set of in-house capabilities are developed that permit the inclusion of this approach into a conceptual design loop. Finally a number of flutter constrained optimizations are performed to understand the impact of imposing flutter constraints in an aircraft design/sizing loop.