In flexible wings, deformation and aerodynamic forces are strongly coupled. However, the high-fidelity computational fluid dynamics and finite element analysis used to estimate structural-aero mechanics are computationally expensive and impractical for parameter studies that consider variable wing geometry. Here, we develop a reduced-order fluid-structure interaction model to determine the forces experienced by a two-dimensional wing undergoing pitch-plunge motion, and use the model to study the effects of variable flexural rigidity on force production. Wing deformation is calculated using the assumed mode method. The fluid model is a modified version of the unsteady vortex lattice method, a technique built on potential flow that treats the wing as a thin airfoil. By varying the thickness distribution of the wing, we can influence the rigidity and aerodynamics of the problem. Using kinematics and material parameters similar to those of a Manduca sexta wing, our model predicts that the maximum lift is generated when the wing is driven at roughly one-third of the its fundamental frequency, which is determined by the thickness distribution. Increasing the average thickness, and therefore the mass and stiffness, resulted in greater lift, though this may come at the cost of increased power consumption. Additionally, the driving-to-natural frequency ratio associated with maximum lift increased slightly with wing thickness. The lift generated by homogeneous wings is strongly affected by wing mass, while the lift of exponentially tapered wings is relatively unchanged. The work described in this paper will lead to more powerful models that can be used with varied geometries and three-dimensional kinematics.