A theoretical approach based on the well-known work of Sigmund to explain the sputtering of surfaces covered with nanoclusters is developed. Predictions of this approach are compared with molecular dynamics results of bombardment of a periodical array of Co nanoislands deposited on a Cu(001) substrate with 1-keV argon ions. Sputtering yield is analyzed distinguishing among particles leaving the target across the nanoisland surface and across the flat substrate surface without nanoparticle above, and the sum of both. Results consider the dependence on two factors: the spacing among nanoislands and the nanoisland height. (C) 2016 Elsevier B.V. All rights reserved.