It has recently been suggested that deformed crustal plateaus on Venus may be composed of felsic (silica-rich) rocks, possibly supporting the idea of an ancient ocean there. However, these plateaus have a tendency to collapse owing to flow of the viscous lower crust. Felsic minerals, especially water-bearing ones, are much weaker and thus lead to more rapid collapse, than more mafic minerals. We model plateau topographic evolution using a non-Newtonian viscous relaxation code. Despite uncertainties in the likely crustal thickness and surface heat flux, we find that quartz-dominated rheologies relax too rapidly to be plausible plateau-forming material. For plateaus dominated by a dry anorthite rheology, survival is possible only if the background crustal thickness is less than 29 km, unless the heat flux on Venus is less than the radiogenic lower bound of 34 mW m −2 mW m − 2 . Future spacecraft determinations of plateau crustal thickness and mineralogy will place firmer constraints on Venus’s heat flux.