Faulting of strike-slip type in vertically inhomogeneous media is analyzed using the classical fracture theory. The analysis makes it possible to get a better insight into various aspects of faulting and earthquakes in real media. The major conclusions are that both low rigidity media and those with regions in which a rapid transition from high to low pore pressure occurs may form barriers for a propagating rupture. The permanent deficit of the driving stress (small or negative stress drop) in sediments that represent the most distinguished class of such media may be one of the main reasons of the generally observed lack of seismicity and rupture suppression there. ¿ 1998 American Geophysical Union