Considering a locking material prior to compaction as a special case of a nonlinearly hardening elastic material, conditions at a discontinuity--a locking front-are analyzed on the basis of three dimensional theory. This study leads to the important result that the major compressive principal stress at a locking front must always be normal to the front, even if the front is not plane. Based on this general result, the effect of a uniform step pressure traveling with subseismic velocity on the surface of a half-space is obtained for the case of a locking material which after compaction has elastic-Coulomb behavior. Such a material acts linearly elastic if the state of stress does not overcome internal friction, but slip occurs if the stresses reach a critical state defined by Coulomb friction. As a special case the solution applies also for a material which is linearly elastic after compaction. The stress, velocity and acceleration histories due to the traveling step pressure are discussed and compared to those in the one dimensional case of a suddenly applied uniform surface pressure.