This paper carries out a transient analysis of the propagation of stress waves generated by time-dependent tangential surface loadings. The problem is solved by representing the concentrated load as a delta-function singularity and applying the boundary conditions to the general solutions to the equations of motion. Expansion in a power series leads to terms which represent successively reflected waves. The complete expressions for the axial shearing stress and axial displacement for an arbitrary forcing function are obtained and curves are shown for step and exponential pulse inputs for an aluminum plate.