Although the low‐order present stress field of most continents is fairly well established, information on paleostress fields is generally sparse. Knowledge of paleostresses is crucial for understanding brittle tectonic reactivation through time. The Indian‐Australian plate lends itself well to a reconstruction of paleostresses, as it has undergone enormous changes in plate‐driving forces through the Tertiary, and there is a rich record of fault reactivation from sedimentary basins. We reconstruct the plate boundary configuration and age‐area distribution of ocean crust around Australia through time to obtain estimates for ridge push, slab pull, and collisional forces acting on the Indian‐Australian plate since the Eocene. Other model parameters we explore are the effects of the Australian‐Antarctic discordance and the mechanical strength of the Australian continental margin. We apply these constraints to model the orientation of the maximum horizontal compressive stress (SHmax) regime for the present, early Miocene, and early Eocene using the commercial software ABAQUS™ along with the optimization software Nimrod/O. We use an elastic two‐dimensional plane stress finite element model with a resolution of ∼0.2° in both longitude and latitude. Realistic elastic parameters representing different rock types and geologic provinces for the Australian continent have been included to model the stress field of a heterogeneous plate. We show that spatially significant rotations of SHmax directions can be modeled as a consequence of perturbations of SHmax in areas of juxtaposed rigid and compliant rheologies. The absence of the collisional Papua New Guinea boundary in the Miocene and reduced ridge push force from the south result in stress directions considerably different from the present. Stress directions over the northern Australian continent in the early Miocene in particular show large disparity with present stress directions. Stress orientations for the Australian plate during the early Eocene are controlled predominantly by ridge push forces arising from spreading in the Wharton Basin in the Indian Ocean and vary substantially with stress directions in the early Miocene and the present because of the drastically different plate geometry and boundary configurations. Fault reactivation histories observed on the northwest shelf of Australia and in the Bass Strait region are consistent with modeled changes in stress directions through time.