  Scale invariance (SI) can in principle be realized in the elastic response of
solid materials. There are two basic options: that SI is a manifest symmetry or
that it is spontaneously broken. The manifest case corresponds physically to
the existence of a non-trivial infrared fixed point with phonons among its
degrees of freedom. We use simple bottom-up AdS/CFT constructions to model this
case. We characterize the types of possible elastic response and discuss how
the sound speeds can be realistic, that is, sufficiently small compared to the
speed of light. We also study the spontaneously broken case using Effective
Field Theory (EFT) methods. We present a new one-parameter family of nontrivial
EFTs that includes the previously known `conformal solid' as a particular case
as well as others which display small sound speeds. We also point out that an
emergent Lorentz invariance at low energies could affect by order-one factors
the relation between sound speeds and elastic moduli.
