  The influence of a strong surface potential on the critical depinning of an
elastic system driven in a random medium is considered. If the surface
potential prevents depinning completely the elastic system shows a parabolic
displacement profile. Its curvature $\mathcal{C}$ exhibits at zero temperature
a pronounced rhombic hysteresis curve of width $2f_c$ with the bulk depinning
threshold $f_c$. The hysteresis disappears at non-zero temperatures if the
driving force is changed adiabatically. If the surface depins by the applied
force or thermal creep, $\mathcal{C}$ is reduced with increasing velocity. The
results apply, e.g., to driven magnetic domain walls, flux-line lattices and
charge-density waves.
