Recent radar images of the mountains of Ishtar Terra, Venus, at approximately 3-km radar resolution show a series of linear bands of alternatively greater andd lesser backscatter; the bands are generally aligned with the topographic strike of the mountain ranges. We test the hypothesis that these band features are tectonic in origin, the product either of folding during lithospheric compression or of block faulting during lithosheric extension. Tested models for folding include uniform elastic and viscous plates overlying inviscid substrates, layered plates, and a viscous half space in which viscosity decreases exponentially with depth. The uniform plate models can produce folds at a dominant wavelength equal to the characteristic spacing between bands on Venus, about 15 to 20 km, if the elastic or high-viscosity layer is, at most, a few kilometers in thickness, though the required compressive stresses are several kilobars in magnitude. For the case of an exponentially decreasing viscosity the skin depth plays the role of layer thickness, and similar results hold. Layered elastic or viscous plates, however, can fold at the required wavelength with subkilobar stresses and, therefore, are favored over uniform plate models. Tested extensional models include graben and horst formation in a surface elastic-brittle layer, imbricate normal faulting, and necking of a surficial layer that is everywhere in a state of extensional failure. The spacing between adjacent extensional features can match the spacing between bands on Venus if the surficial brittle layer is no more than a few kilometers in thickness. Both compressional and extensional models for bandd formation are therefore consistent with radar images of Venus mountain ranges at the image resolution presently available. Additional evidence, however, including the linearity and continuity of individual bands, the relationship between band trends and topographic contours in some regions near the ends of mountain ranges, and the very different manifestations of lithospheric extension in other highland areas of Venus, leads us to favor the hypothesis that banded terrain formed contemporaneously with the mountain ranges of Ishtar Terra as a result of horizontal compression of the Venus lithosphere. Independent arguments on the thermal structure of the Venus crust and the mechanical behavior of crustal rocks as a function of temperature indicate that the elastic lithosphere of Venus is approximately 1-10 km thick. We therefore suggest that the surficial layer of elastic-brittle or high-viscosity behavior required for either the compressional or extensional models may in fact be the elastic lithosphere of the Venus highlands at the time of band formation.