We have fabricated self-organized ∼30-nm-wide Cu lines on glass and Si(100) substrates by Ar beam etching the Cu/substrate interfaces. We deposited thin Cu layers on the substrates and etched the deposited layer by a neutralized Ar ion beam at a grazing angle of incidence. At the stage when almost all Cu is removed by etching, we have observed Cu lines on the substrate. The lines orientation is entirely controllable through the experiment geometry and the lines are basically similar on glass and Si substrates. By atomistic Monte Carlo simulations, we have demonstrated that the Cu lines result from the self-organized morphologies that develop on Cu surfaces during sputter etching. To better understand ways to control the process we have investigated, by simulations, the line width as a function of the removed depth, surface diffusivity, and Ar beam flux. We have concluded that the sputter etch technique offers a unique opportunity to fabricate controlled arrays of Cu lines on substrates.