The mechanical response of amorphous materials to shear stress is analogous to the dielectric or magnetic response to an electric or magnetic field. The spectrum consists of a resonance and a relaxation. The resonance is at high frequency, typically of the order of one teraherz, and corresponds to a dipolar vibration without a thermally stimulated rotation. It is linear in the stress, relatively insensitive to temperature, and is sometimes called a diaelastic effect. The relaxation corresponds to a thermally stimulated jump with a strong temperature-dependent relaxation time (which can vary over 18 orders of magnitude), and is sometimes called a paraelastic effect. Liquids at high temperature strongly attenuate shear waves. Supercooled liquids have a frequency-dependent shear modulus G with low frequency limit G(0)=0 and high frequency limit called G ∞. Because of this, the relaxation strengths are enormous. This is in contrast to most damping effects, where the relaxation strength is linear in defect concentration. Frozen liquids (glasses) have rigidities intermediate between liquids and crystals. For glasses at temperatures near the glass temperature T g, the maximum damping at ωτ=1, where τ is the Maxwell relaxation time, occurs in the torsion pendulum range. For fragile amorphous materials, where temperatures just above T g can be used, the maximum can be tuned to frequencies as high as 10 MHz by material selection. The Interstitialcy Theory provides an atomistic interpretation of the principal characteristic and universal mechanical (and electrical) properties of glasses and supercooled liquids. As dislocations carry the deformation in crystals, interstitials are the basic microscopic elements carrying the deformation in glasses near and above the glass temperature. Interstitialcies are the ‘dipoles’ which provide a Snoek peak, which is an important component of the principal alpha peak, accounting for the high frequency part of the peak.