In this paper, numerical studies of friction-induced dynamic instabilities, in particular, stick-slip sliding of rocks, are presented. Of special interest is the importance of normal compliance of the interface and associated normal vibrations in the occurrence of dynamic instabilities. To clearly illustrate this importance, the interface is represented by the Oden-Martins constitutive model which does not exhibit explicit velocity or slip dependence of friction. This friction model is utilized in the context of a rather simple rigid body model to perform numerical studies representative of granite blocks in relative sliding at very slow overall velocities. The model represents a common experimental setting that has been used to study stick slip of sliding rock blocks. To capture the stick-slip phenomenon the detailed dynamic response of this system is modeled numerically. These studies indicate the importance of the normal compliance of the interface on the stability of sliding. In particular, dynamic coupling of the degrees of freedom contributes to dynamic instability of the system and can cause stick-slip motion. Both stable and unstable sliding are predicted and examined.¿ 1997 American Geophysical Union