Measurements made during the Ross Ice Shelf Geophysical and Glaciological Survey (RIGGS, 1973–78) are used to determine the large-scale rheological conditions of the Ross Ice Shelf, Antarctica. Our method includes a numerical ice-shelf model based on the stress-equilibrium equations and control theory. We additionally perform a few tests on simplified geometries to investigate the precision of our method. Our results consist of a map of the depth-averaged viscosity of the central part of the Ross Ice Shelf to within an uncertainty of 20%. We find that the viscosity variations are consistent with Glen’s flow law. Application of a more realistic flow law in our study provides little enhancement of ice-shelf model accuracy until uncertainties associated with basal melting conditions and with temperature profiles at inflow boundaries are addressed. Finally, our results suggest a strong viscosity anomaly in the west-central part of the ice shelf, which is interpreted to be associated with changes in the dynamics of Ice Stream A or B at least 1000 years ago. This feature conforms to the prevailing notion that the West Antarctic ice streams are unsteady.