The principal conduits for magma transport within rift zones of basaltic volcanoes are steeply dipping dikes, some of which feed fissure eruptions. Elastic displacements accompanying a single dike emplacement elevate the flanks of the rift relative to a central depression. Concomitant normal faulting may transform the depression into a graben thus accentuating the topographic features of the rift. If eruption occurs the characteristic ridge-trough-ridge displacement profile changes to a single ridge, centered at the fissure, and the erupted lava alters the local topography. A well-developed rift zone owes its structure and topography to the integrated effects of many magmatic rifting events. To investigate this process we compute the elastic displacements and stresses in a homogeneous, two-dimensional half-space driven by a pressurized crack that may breach the surface. A derivative graphical method permits one to estimate the three geometric parameters of the dike (height, inclination, and depth-to-center) and the mechanical parameter (driving pressure/rock stiffness) from a smoothly varying displacement profile. Direct comparison of measured and theoretical profiles may be used to estimate these parameters even if inelastic deformation, notably normal faulting, creates discontinuities in the profile. Geological structures (open cracks, normal faults, buckles, and thrust faults) form because of stresses induced by dike emplacement and fissure eruption. Theoretical stress states associated with dilation of a pressurized crack are used to interpret the distribution and orientation of these structures and their role in rift formation. ?? 1983.