The construction of a large volcanic edifice at Earth's surface generates stresses in the upper crust whose magnitude is comparable to those of tectonic stresses and overpressures within a magma chamber. We study how this affects eruption behavior. Analytical calculations are carried out in two dimensions for a cylindrical reservoir with an internal overpressure in an elastic half-space with an edifice at the surface. Different edifice shapes are considered, from shield volcanoes with gentle slopes to stratovolcanoes with steeper flanks. Without an edifice at the top, the hoop stress at the cavity walls reaches a maximum at two symmetrical points at some distance from the axis, away from the top of the chamber. With an edifice at the top, the maximum is reached at the top of the chamber, just beneath the edifice summit. This implies preferential failure of chamber walls at the axis and hence the focussing of volcanic activity through a central vent system. Tensile failure of the cavity walls occurs for a critical value of magma overpressure which depends on the dimensions of the edifice and on the depth and size of the cavity. For a small magma chamber beneath a large stratovolcano, the magmatic overpressure at the onset of eruption increases as the edifice grows and decreases following edifice destruction. These effects may explain why pressures recorded in phenocryst assemblages at Mount St. Helens, have varied over the past 4000 years as the edifice went through successive phases of growth and destruction.