Recent work shows that linked gramicidin channels may have much longer lifetimes than single channels. We establish that the stabilization of the individual channels can be caused by membrane-mediated elastic interactions between such inclusions. In linear elastic theory, interaction can be rigorously described in terms of coupled harmonic oscillators. We determine the "effective spring constants'' for various assemblies using the smectic bilayer model. We consider a range of aggregates; in clusters, channel lifetimes may increase by several orders of magnitude, an effect that is especially pronounced for a channel with many near neighbors. (C) 2003 American Institute of Physics.