Despite extensive documentation of plastic deformation processes in micro-sized samples, there is up to now no clear understanding of the mechanisms governing plastic flow in nanoscale systems. Here, using a quartz-tuning fork based Atomic Force Microscope, we combine electrical and rheological measurements on nanoscale gold junctions, and study the onset of plastic flow in those model atomic-sized systems. By submitting the junction to increasing sub-nanometric deformations, we uncover a transition from an elastic regime to a plastic regime. Increasing deformations even further leads to the complete shear melting/liquefaction of the junction. This typology is reminiscent of the behavior of macroscopic complex fluids, here uncovered for a “molecular foam”. We rationalize and interpret our results in the framework of a harmonically driven Frenkel-Kontorova model. Our measurements allow us to measure the critical yield force governing the onset of plastic flow in the junction, as a function of size. In those molecular systems, plasticity is limited by the direct sliding of atomic planes under shear, as expected for dislocation-free systems.