A significant fraction of the volcanism on the Earth's surface cannot be associated with plate margin processes. The mantle plume hypothesis is one explanation for this volcanism. Convective plumes beneath rigid plates could be the result of turbulent thermal convection within the upper mantle. Although the hypothesis of nearly fixed mantle plumes is reasonably successful in explaining the direction and velocity of migration of intra-plate volcanism, there are a number of difficulties. It is particularly difficult to explain continued volcanism over extended linear distances. An alternative hypothesis for intra-plate volcanism is that magmas flow to the surface through lithospheric fractures. In this case intra-plate volcanism would be associated with tensional tectonics. Intra-plate volcanism and seismicity in Africa and the western United States are discussed in terms of these hypotheses.