The nonlinear characteristics of inverted flags, otherwise known as cantilevered plates in a reverse steady axial flow, is investigated. A Hamiltonian framework is employed to derive the nonlinear integro-differential equation of motion in terms of the rotation angle of the mid-plane with respect to the longitudinal axis of the flag. This allows for reliable predictions even at very large deflection amplitudes. The effect of a finite aspect ratio as well as the presence of an initial curvature along the length of the plate are taken into account in the modelling. The Galerkin modal decomposition technique along with various numerical schemes such as a full Newton method as well as a shooting technique are implemented to construct the bifurcation response diagram of the system as the flow velocity varies. As opposed to the case of flag-type cantilevered plates in steady axial flow, the system undergoes a static divergence via a subcritical pitchfork bifurcation followed by a saddle-node bifurcation. Extensive numerical simulations are performed to investigate the effect of the aspect ratio and initial curvature amplitude on the nonlinear response of the system. The possibility of a supercritical pitchfork bifurcation is also explored. The results of the current model are compared to and validated against measurements reported in the literature.