A similarity solution is derived for the two-dimensional propagation of a liquid-filled crack. This solution includes both the flow problem within the crack and the fracture problem through a stress intensity factor. The results are applied to the emplacement of dikes and sills and to the migration of magma through the lithosphere. We show that for these applications the propagation of the fracture is limited by the viscosity of the magma; the fracture resistance of the elastic medium can be neglected. Limitations on propagation due to magma solidification during emplacement are also considered. As a typical example for the emplacement of a dike or sill, we conclude that a magma with a viscosity of 102 Pa s can be injected into a crack with a length of 2 km and a width of 0.5 m in a period of 15 min; the velocity of fracture propagation is about 0.5 m s-1. We also conclude that a propagating, liquid-filled crack is a viable mechanism for the migration of magma through the lithosphere.