We examine the possible ascent of alkali basalt magma containing 2 wt percent water through a dike and into a horizontal subsurface drift as part of a risk assessment for the proposed high-level radioactive waste repository beneath Yucca Mountain, Nevada, USA. On intersection of the dike with the low pressure, horizontal drift, the ascending magma will be diverted into the drift. The fragmenting mixture expands down the drift to reach speeds of order 100--300 m/s. After this initial disruptive activity, parts of the repository can be filled with magma within a matter of hours until a pathway is found to allow the magma to vent. Magma flow through the drift network will cause intense heating of any waste canisters located along the pathway between the dike and the surface conduit. The assessments suggest a greater number of waste packages may be adversely affected than previously recognized.