Glaciers in the tropical highlands are important and highly sensitive indicators of global climate change over different time scales. We apply a physically based, 2-D, glacier model to reconstruct steady-state glacier forms and mass distributions for a range of tropical climatic conditions in the Cordillera Blanca, Peru (8-10°S) and the Cordillera Real, Bolivia (16° S). The model is based on gridded digital elevation data, computes the effects of topography on the largest component of surface energy balance, shortwave solar insolation, calculates 2-D, in the horizontal-plane, distribution of snow accumulation using a surface mass and energy balance approach, and reconstructs resultant glacier shape with a 2-D flow model. We are able to reconstruct modern glacier extent to match satellite imagery using climate data from the separate regions including current observations at glacier elevations, and compute a modem equilibrium line at ~5000 m. We then apply the model in an inverse approach to infer sets of paleoclimate conditions for late Pleistocene moraine positions mapped in specific valleys with global positioning system positions and dated by radiocarbon dates on lake and peat sediments for locations in the Queshque Valley in the Cordillera Blanca and the Zongo-Milluni Valleys in the Cordillera Real. Our results show a range of climate situations possible for the existence of the delineated glaciers in the Queshque and Zongo-Milluni Valleys. For the Zongo Valley, we also find that 6.5 times more precipitation is needed to grow to the same dated moraine as the adjoining Milluni Valley with a -4.25 °C temperature change.