A volcanic edifice exerts a large load at Earth's surface and modifies the stress field at depth. We investigate how this affects upward dyke propagation towards the surface. For given edifice dimensions and pressure conditions in the deep magma source, there is a critical density threshold above which magmas cannot reach the surface. This density threshold is a decreasing function of edifice height. For edifice heights in the range 0-3000 m, the density threshold spans the density range of common natural magmas (between 2700 and 2300 kg m−3). With time, differentiation in a magma chamber generates increasingly evolved magmas with decreasing densities, which favours eruption. However, the edifice grows simultaneously at the surface, which counterbalances this effect. The general tendency is to gradually prevent more and more evolved magmas from reaching the surface. A volcanic edifice acts as a magma filter which prevents eruption and affects the chemical evolution of the chamber through its control on magma withdrawal. Thus, one may not consider that eruption products are random samples of an evolving magma reservoir. The partial destruction of an edifice may lead to renewed eruption of primitive and dense magmas.