The response of a layered half-space to a progressing normal surface pressure is evaluated. The half-space consists of a single layer of a locking material that acts elastically after compaction, and an underlying elastic material. The surface pressure moves with a constant velocity V, which is subseismic with respect to the speed of wave propagation in both the upper layer after compaction and the underlying half-space. It is assumed that a steady- state exists with respect to a coordinate axis attached to the moving load. The essentially subseismic layer--subseismic half-space geometry leads to an elliptic problem that is solved by a finite difference iterative technique. A computer program for evaluating stresses and velocities at points in the medium is available and results are presented for a typical configuration of interest.