The manner in which magma enters and leaves a magma reservoir is a fundamental aspect of magmatic activity. A quantitative model is developed to evaluate the variation of stress acting on the wall of a magma reservoir as a function of depth. Factors assessed include the size of the reservoir, its depth of burial, the strength of the country rocks, and the variation with depth of the densities of the magma and country rocks. It is shown that small magma reservoirs (with halfheights less than 1 km) centered at levels of neutral buoyancy can grow in all directions with nearly equal ease by injecting dikes into their surroundings at the sites of wall ruptures. In larger reservoirs (with half-heights greater than 2 km), however, the stress required to cause wall failure is much less at the depth corresponding to the center of the reservoir than it is near the top or bottom. Thus, larger reservoirs are likely to grow predominantly sideways by lateral dike injection. In these cases, vertical growth will not be important unless significant accumulation of low-density material can occur in the upper part of the reservoir. The formation of a low-density layer, due to gas exsolution or chemical differentiation of the magma, can facilitate failure of the roof and upward dike migration from a mature reservoir. As the reservoir grows and evolves through time, the increasing magma pressure head at the depth corresponding to the center of the reservoir means that the amount of gas exsolution or chemical differentiation required to allow the occurrence of vertical dike emplacement also increases. Ultimately, a vertical reservoir size is reached beyond which the excess stress required to cause lateral dike injection is so much less than that required to cause vertical injection that essentially no further vertical growth of the reservoir will occur. The reservoir will thus develop a more laterally elongate shape with time. The final aspect ratio will then depend mainly on the supply rate of magma to the reservoir from the mantle.