Magma-driven fractures must be an important mechanism for the transport of magma through the crust and lithosphere. Dikes are pervasive throughout the crust and clearly play an important role in active volcanoes. A magma fracture is the only mechanism that allows sufficiently high magma velocities to prevent complete solidification during transport through cold country rock. The analysis of magma-driven fractures is complex because it involves flow in the fracture (often turbulent), the elastic deformation of the country rock surrounding the eracture, and the propagation of the fracture. For vertically propagating magma fractures, buoyancy forces may be the dominant driving mechanism. In order to simplify the analysis of this problem we neglect the elastic distortion of the country rock and the fracturing process. We consider a buoyant fluid initially in an elliptical two-dimensional cavity. The shape of the upwardly deforming cavity is shown to satisfy the nonlinear kinematic wave equation. For laminar flow the cavity initially deforms but does not move upward. At a critical time the solution near the top of the crack becomes multivalued indicating the presence of an upwardly propagating shock wave. The tail of the upwardly propagating crack closes but does not move upwards. Solutions have also been obtained for turbulent flow. Velocities of upward propagation for appropriate parameter values indicate this mechanism can explain the observed characteristics of kimberlite eruptions. Inclusion of elastic and fracture properties will determine the structure of the shock wave, that is, the crack tip, but would not effect the applicability of our solution. ¿ American Geophysical Union 1990