We study dynamic rupture propagation on flat faults using 2D plane strain models featuring strongly rate-weakening fault friction (in a rate-and-state framework) and off-fault Drucker–Prager viscoplasticity. Plastic deformation bounds stresses near the rupture front and limits slip velocities to ∼10 m/s, a bound expected to be independent of earthquake magnitude. As originally shown for ruptures in an elastic medium (Zheng and Rice, 1998), a consequence of strongly rate-weakening friction is the existence of a critical background stress level at which self-sustaining rupture propagation, in the form of self-healing slip pulses, is just barely possible. At higher background stress levels, ruptures are cracklike. This phenomenology remains unchanged when allowing for off-fault plasticity, but the critical stress level is increased. The increase depends on the extent and magnitude of plastic deformation, which is influenced by the orientation of the initial stress field and the proximity of the initial stress state to the yield surface.