We perform two-dimensional plane-strain finite-difference calculations of dynamic rupture along an interface separating different elastic media. The calculations extend earlier results of Andrews and Ben-Zion (1997) who found a self-sustaining narrow slip pulse associated with dynamic reduction of normal stress along a material interface governed by constant friction, in agreement with Weertman (1980). The pulse propagates in a wrinklelike mode having remarkable dynamic properties that may be relevant to many geophysical phenomena. Here we examine the range of values of elastic parameters, friction coefficient, and strength heterogeneities allowing for the existence of the wrinklelike pulse. Rupture is initiated in the simulations by imposed slip in a limited space-time domain. Outside the region of the imposed slip, the pulse becomes narrower and higher with propagation distance along the interface. The strength of the wrinklelike pulse increases with S-wave velocity contrast up to a maximum at about 35% contrast. Beyond such a velocity contrast, there is no solution for a generalized Rayleigh wave along a material interface, and the strength of the pulse decreases. However, the wrinklelike pulse can still propagate in a self-sustaining manner for larger velocity contrasts. For a fixed S-wave velocity contrast, the strength has little dependence on density contrast or Poisson's ratio, but the pulse strength increases rapidly with increasing coefficient of friction. Stress and strength heterogeneities with small correlation length have little effect on the pulse, while long wavelength heterogeneities reduce the strength of the pulse. The high mechanical efficiency of the wrinklelike pulse suggests that earthquake ruptures may favor such mode of failure when possible.