During the Last Glacial Maximum (LGM), the Patagonian Ice Sheet (PIS) was the largest Quaternary ice mass in the Southern Hemisphere outside of Antarctica. Although the margins of the LGM ice sheet are now well established through end-moraine mapping and dating, apart from a few modelling and empirical studies, there remains a lack of constraint on its thickness and three-dimensional configuration. Here, we provide a high-resolution steady-state model reconstruction of the PIS at its maximum - LGM - extent applied using Nye's perfect-plastic ice rheology. The yield-strength parameter for the perfect-plastic flow model was calibrated against independent empirical reconstructions of the Lago Pueyrredón Glacier, where the former vertical extent of this major outlet glacier is well constrained by cosmogenically-dated trimlines and lateral and end-moraine limits. Using this derived yield-strength parameter, the perfect-plastic model is then applied to multiple flowlines demarking each outlet across the entirety of the PIS in a GIS framework. Our results reveal that the area of the PIS was ∼504,500 km2 (±8.5%) with a corresponding modelled ice volume of ∼554,500 km3 (±10%), equivalent to ∼1.38 m (±10%) of eustatic sea-level lowering at the LGM. Maximum surface elevation was at least 3500m asl although the majority of the ice sheet surface was below 2500 m asl. We find that our ice sheet reconstruction is in good general agreement with previous estimates of net PIS volume derived from transient modelling studies. We attribute the slightly lower aspect-ratio of our ice sheet (and its concomitant 5% reduction in volume and sea-level equivalent) to the lower yield strength applied, based on more temperate and dynamic ice sheet conditions.