We formulate a model for rift propagation which treats the rift as a crack in an elastic plate which is filled from beneath by upwelling viscous asthenosphere as it lengthens and opens. Growth of the crack is driven by either remotely applied forces or the pressure of buoyant asthenosphere in the crack and is resisted by viscous stresses associated with filling the crack. The model predicts a time for a rift to form which depends primarily on the driving stress and asthenosphere viscosity. For a driving stress on the order of 10 MPa, as expected from the topography of rifted swells, the development of rifts over times of a few Myr requires an asthenosphere viscosity of 1016 Pa s (1017 poise). This viscosity, which is several orders of magnitude less than values determined by postglacial rebound and at least one order of magnitude less than that inferred for spreading center propagation, may reflect a high temperature or large amount of partial melting in the mantle beneath a rifted swell. ¿ American Geophysical Union 1989