Laser-driven similar to 1 GPa shock waves are used to dynamically compress self-assembled monolayers (SAMs) consisting of octadecanethiol (ODT) on An and Ag, and pentanedecanethiol (PDT) and benzyl mercaptan (BMT) on Au. The SAM response to < 4 ps shock loading and similar to 25 ps shock unloading is monitored by vibrational sum-frequency generation spectroscopy (SFG), which is sensitive to the instantaneous tilt angle of the SAM terminal group relative to the surface normal. Arrival of the shock front causes SFG signal loss in all SAMs with a material time constant < 3.5 ps. Thermal desorption and shock recovery experiments show that SAMs remain adsorbed on the substrate, so signal loss is attributed to shock tilting of the methyl or phenyl groups to angles near 90 degrees. When the shock unloads, PDT/Au returns elastically to its native structure whereas ODT/Au does not. ODT evidences a complicated viscoelastic response that arises from at least two conformers, one that remains kinetically trapped in a large-tilt-angle conformation for times > 250 ps and one that relaxes in similar to 30 ps to a nearly upright conformation. Although the shock responses of PDT/Au, ODT/Ag, and BMT/Au are primarily elastic, a small portion of the molecules, 10-20%, evidence viscoelastic response, either becoming kinetically trapped in large-tilt states or by relaxing in similar to 30 ps back to the native structure. The implications of the observed large-amplitude monolayer dynamics for lubrication under extreme conditions of high strain rates are discussed briefly.