Many plasma applications involve the plasma coming into contact with a liquid surface. Previous analyses of the stability of such liquid surfaces have neglected the presence of the sheath region between the bulk plasma and the liquid. Large electric fields, typically in excess of several MV m−1, and strong ion flows are present in this region. This paper considers a linear perturbation analysis of a liquid-sheath interface in order to find the marginal condition for instability. This condition shows that molten metal surfaces in tokamak edge plasmas are stable against the electric field, if a normal sheath is formed, due to the impact of ions on the surface. The stabilization of the liquid surface by ion bombardment is encouraging for the ongoing development of plasma-liquid technologies.