Many volcanic structures have a regular geometrical form that suggests a simple and universal mechanism for the growth. We suggest that the surface of these volcanic structures is a surface of constant hydraulic potential. When an eruption begins, it follows a path to the point on the surface that has the minimum hydraulic resistance. This resistance includes both the brictional resistance to the flow and the gravimetric potential associated with elevation. We determine the shape of a two-dimensional volcanic edifice formed from a line source and compare the shape with bathymetric profiles across several aseismic ocean ridge. We also compare the predicted shape of an axisymmetric volcanic edifice formed from a point source with several profiles from the Cascade Range in the western United States and with a number of volcanic islands and seamounts in the Pacific.