The structure, tectonics, and evolution of large volcanoes on Venus, as revealed by data from the Magellan mission, appear to be distinct from those on Earth and Mars. To determine the conditions and processes that account for these differences, we model the evolution of stress and deformation in growing volcanic edifices on Venus using the finite element method. Large volcanoes on Venus are characterized by topographically prominent conical edifices surrounded by relatively flat flow aprons. The surfaces of both edifice and apron consist dominantly of radially oriented flows. Tectonic features, usually the surface expression of shallowly intruded dikes, also have predominantly radial orientations. Features similar to Hawaiian-style linear rift zones or large-scale flank failure, common on large volcanoes on Earth and Mars, are absent. By comparing predictions of faulting for models with detached and welded basal boundary conditions with the observed tectonic features, we determine that a welded condition is more likely. Horizontal compressive stresses transmitted into edifices across welded basal boundaries are inversely proportional to elastic lithosphere thickness Te. Contravening stress increments from magma chamber expansion, differential thermal contraction, or buoyant loading from beneath the crust or lithosphere are required to reorient principal stresses in the edifice so that magma ascent and radial dike formation are favored. Incremental volcano growth results in stress distributions that decrease with height in the edifice. Dike intrusion is easiest in the uppermost (youngest) layers, consistent with the observed shallow radial dikes on Venus volcanoes. Small values of Te greatly inhibit the formation of large shields, in that conical edifice topography cannot be supported and large contravening stresses are required for further growth. Large volcano formation is much more likely at large Te, where more moderate contravening stresses are sufficient for growth. The near-surface manifestation of mantle upwelling on Venus may thus depend on Te in that the response to upwellings beneath thin or nonexistent lithosphere is likely to be dominantly ductile, leading to the formation of coronae, but a thick elastic lithosphere is required to support the growth of the largest volcanoes. The transitional value of Te between these modes of evolution likely depends on the horizontal scale of the upwelling. ¿ 1998 American Geophysical Union