The tribology of a sliding elastic continuum in contact with a disorde
red substrate is investigated analytically and numerically via a bead-
spring model. The deterministic dynamics of this system exhibits a dep
inning transition at a finite driving force, with complex spatial-temp
oral dynamics including stick-slip events of all sizes. These behavior
s can be understood completely by mapping the system to the well-known
problem of a directed path in higher-dimensional random media.