Using in situ imaging, we report surface fold formation and fluidlike flow instabilities in sliding of annealed copper. We demonstrate using simulations that folding is principally driven by grain-induced plastic instability. The phenomenon shows remarkable similarities with Kelvin-Helmholtz-type flow instabilities in fluids. While such instabilities have been conjectured to exist in sliding interfaces at the nanoscale, we find vortices and folding in metals at the mesoscale. The occurrence of folds impacts many applications, including surface generation processes and tribology.