This paper describes a new concept referred to here as "energy sinks" as an alternative to conventional methods of vibration absorption and damping. A prototypical energy sink envisioned here consists of a set of oscillators attached to, or an integral part of, a vibrating structure. The oscillators that make up an energy sink absorb vibratory energy from a structure and retain it in their phase space. In principle, energy sinks do not dissipate vibratory energy as heat in the classical sense. The absorbed energy remains in an energy sink permanently (or for sufficiently long durations) so that the flow of energy from the primary structure appears to it as damping. This paper demonstrates that a set of linear oscillators can collectively absorb and retain vibratory energy with near irreversibility when they have a particular distribution of natural frequencies. The approach to obtain such a frequency distribution is based on an optimization that minimizes the energy retained by the structure as a function of frequency distribution of the oscillators in the set. The paper offers verification of such optimal frequency spectra with numerical simulations and physical demonstrations. (c) 2005 Acoustical Society of America.