Topographic flexure in response to vertical loads reveals key lithospheric properties, including elastic thickness and the heat flow from the interior. Flexural stresses may also control volcano morphology. One previous study predicted that steep-sided domes on Venus usually form where the elastic thickness is ~15-40 km. We surveyed flexural signatures around steep-sided domes and confirmed this hypothesis. We determined elastic thickness from topographic profiles with a curve-fitting algorithm and a plate bending model in Cartesian and axisymmetric geometry. We used a yield stress envelope to convert elastic thickness and plate curvature into mechanical thickness and surface heat flow. The average elastic thickness for domes not near coronae is ~30 km, corresponding to a heat flow of ~60 mW/m². Coronae on Venus are typically associated with elastic thicknesses of <10-15 km. Domes near coronae yielded elastic thicknesses in this range, and higher heat flows than domes not near coronae.