A thin-shell formulation for computing stress distributions on the surfaces of one-plate planets is developed. The lithospheric model includes laterally varying density anomalies at two depths, corresponding to undulations on a crust-mantle boundary and variations in upper mantle density. For a given set of model parameters, values for the vertical displacement, crustal thickness anomaly and mantle density anomaly, required to satisfy the topographic and gravitational boundary conditions are computed, along with the resulting stress field. The computed stresses can then be compared to stress directions inferred from observed tectonic features. This formulation is used to study loads on Venus's lithosphere, and it is found that most highland areas appear to have benn formed in a state of isostasy or by uplift, with a significant portion of their support probably derived from dynamic processes in the mantle. A possible exception is Ishtar Terra, whose circumferential mountain belts are most consistent with a radially compressive stress regime generated by flexural loading. Reasonable lithospheric models predict low-density mantle beneath Atla, Beta, Eisila, Thetis, and Tethus Regiones and thick crust accompanied by higher-density mantle under Ishtar Terra and Ovda Regio. Thus western Aphrodite Terra appears to be more closely related to Ishtar than to the rest of the equatorial highlands. These results favor a hot spot model of Venus tectonics in which Beta, eastern Aphrodite, Eisila, and Tethus are expected to be relatively young and thermally active, while Ovda and Ishtar should be older and less active.