This paper is devoted to the modeling of dynamic triggering of earthquakes by a sinusoidal plane wave. I consider a 2D antiplane finite fault of length L under a linear slip-dependent friction law, characterized by a non-dimensional weakening parameter &bgr;. The finite fault is perturbed by an incident sinusoidal stress wave of wavelength &lgr; and amplitude a. The positive pulse of the wave loads the fault and promotes the instability, while the negative pulse tends to heal the initiation process that may lead to the rupture. The occurrence of triggering depends on the balance between the loading terms and the intrinsic mechanics of the fault. Both amplitude and frequency exert a clock advance effect on the triggering. A threshold in frequency for the incident wave to trigger the rupture is revealed, which depends on the non-dimensional weakening parameter &bgr; and separates a nontriggering domain with stable slip from a triggering domain with unstable slip. ¿ 2001 American Geophysical Union