The introduction of material into the void of honeycomb-like structures, such as foam, viscoelastic or particulate filling, has been credited with improving the damping properties of the honeycombs. Optimisation of such damping inserts has been investigated, and indicates that partial occupation of the void could be more efficient, on a density basis, than full filling. The main goal of this study is to explore fully damping in honeycomb cells with inserts from the point of view of minimal increase in density and location of inserts. In this paper, damping of vibrations in the plane is investigated using analytical, finite element and topological optimisation methods to find the best locations of a damping insert within the cell. (C) 2013 Published by Elsevier Ltd.