The response of organic polymers and proteins including poly(methyl methacrylate) (PMMA) and the protein bovine serum albumin (BSA) to a short duration 4.5 GPa shock pulse, termed a "nanoshock", is studied using ultrafast coherent Raman spectroscopy (CARS) to monitor density-dependent vibrational frequency shifts of a dye molecule probe. In conventional shock compression experiments, a two-part response of PMMA to fast compression is usually explained with a phenomenological viscoelastic model. The molecular basis for this two-part response is discussed here using an energy landscape model to describe large-amplitude structural relaxation of shocked supercooled liquids. The polymers and the protein show an instantaneous response to the steeply rising shock front, viewed as a vertical transition to a new region of the energy landscape with radically different topography. A slower similar to 300 ps response is also observed, attributed to large-amplitude structural relaxation along the rugged shocked energy landscape. A viscoelastic model is used to determine an effective shock viscosity eta approximate to 3 Pa.s for the solid samples. This extremely small value (compared to eta > 10(12) Pa.s expected for supercooled liquids) is explained as a result of the very large strain rate and the extensive plastic deformation, which causes even seemingly rigid solids to flow. After the short duration (similar to 2 ns) nanoshock unloads and the samples become frozen, for at least tens of nanoseconds, in a state where the dye vibrational shift indicates a negative pressure of about -1 GPa. The negative pressure means the local density near the dye has decreased, the sample has become more permeable, and the sample is unstable to spontaneous expansion of the polymer chains. The energy landscape model provides a framework for understanding the fast cycle of compression and expansion and how to optimize the generation and detection of large-amplitude structural relaxation processes.