Pulses of slip velocity can propagate on a planar interface governed by a constant coefficient of friction, where the interface separates different elastic materials. Such pulses have been found in two-dimensional plane strain finite difference calculations of slip on a fault between elastic media with wave speeds differing by 20%. The self-sustaining propagation of the slip pulse arises from interaction between normal and tangential deformation that exists only with a material contrast. These calculations confirm the prediction of Weertman [1980] that a dislocation propagating steadily along a material interface has a tensile change of normal traction with the same pulse shape as slip velocity. The self-sustaining pulse is associated with a rapid transition from a head wave traveling along the interface with the S wave speed of the faster material, to an opposite polarity body wave traveling with the slower S speed. Slip occurs during the reversal of normal particle velocity. The pulse can propagate in a region with constant coefficient of friction and an initial stress state below the frictional criterion. Propagation occurs in only one direction, the direction of slip in the more compliant medium, with rupture velocity near the slower S wave speed. Displacement is larger in the softer medium, which is displaced away from the fault during the passage of the slip pulse. Motion is analogous to a propagating wrinkle in a carpet. The amplitude of slip remains approximately constant during propagation, but the pulse width decreases and the amplitudes of slip velocity and stress change increase. The tensile change of normal traction increases until absolute normal traction reaches zero. The pulse can be generated as a secondary effect of a drop of shear stress in an asperity. The pulse shape is unstable, and the initial slip pulse can change during propagation into a collection of sharper pulses. Such a pulse enables slip to occur with little loss of energy to friction, while at the same time increasing irregularity of stress and slip at the source. Copyright 1997 by the American Geophysical Union.