  We consider a discrete and a continuum model for the propagation of a
curvature sensitive interface in a time independent random medium. In both
cases we suppose that the medium contains obstacles that act on the propagation
of the interface with an inhibitory or an acceleratory force. We show that the
interface remains bounded for all times even when a small constant external
driving force is applied. This phenomenon has already been known when only
inhibitory obstacles are present. In this work we extend this result to the
case of, for example, a random medium of random zero mean forcing.
