Antarctic ice shelves in the Amundsen Sea embayment are vulnerable to rapid disintegration, the dynamics of which depend strongly on the rate of melting of the ice shelf. In particular, melt rates in the grounding zone - where ice transiently makes contact with the bedrock - have proven difficult to measure using remote methods which rely on remote measurements of the ice freeboard and an application of the hydrostatic approximation. Here, we extend existing remote observations of melt rates into the grounding zone by incorporating a model of the elastic flexure of ice shelves. The numerical model is tested against existing analytical models, and then demonstrated on select ice shelves in the Amunsdsen sea embayment. Melt rates are found which are comparable with existing hydrostatic estimates away from the grounding zone, but are more continuous within the region of transient contact with the bedrock.