We use the Richtmyer-Meshkov instability (RMI) at a metal-gas interface to infer the metal's yield stress (Y) under shock loading and release. We first model how Y stabilizes the RMI using hydrodynamics simulations with a perfectly plastic constitutive relation for copper (Cu). The model is then tested with molecular dynamics (MD) of crystalline Cu by comparing the inferred Y from RMI simulations with direct stress-strain calculations, both with MD at the same conditions. Finally, new RMI experiments with solid Cu validate our simulation-based model and infer Y~0.47 GPa for a 36 GPa shock.