Low-fidelity aerostructural optimization routines have often focused on determining the optimal spanloads for a given wing configuration. Several analytical approaches have been developed that can predict optimal lift distributions on rectangular wings with a specific payload distribution. However, when applied to wings of arbitrary geometry and payload distribution, these approaches fail. Increasing the utility and accuracy of these analytical methods can result in important benefits during later design phases. In this paper, an iterative algorithm is developed that uses numerical integration to predict the distribution of structural weight required to support the bending moments on a wing with arbitrary geometry and payload distribution. It is shown that the algorithm’s predictions for the structural weight of a rectangular test wing match those found using an analytical approach. The structural weight distribution for a spanwise-constant non-structural weight distribution is also found. Coupling the algorithm with an optimization routine, the optimal lift distributions for the rectangular test wing are found and are shown to match analytical results. Finally, the optimal lift distributions for a test wing configuration with a spanwise-constant non-structural weight distribution are found using the algorithm.