  We present an elastic constitutive model of gravity where we identify
physical space with the mid-hypersurface of an elastic hyperplate called the
"cosmic fabric" and spacetime with the fabric's world volume. Using a
Lagrangian formulation, we show that the fabric's behavior as derived from
Hooke's Law is analogous to that of spacetime per the Field Equations of
General Relativity. The study is conducted in the limit of small strains, or
analogously, in the limit of weak and nearly static gravitational fields. The
Fabric's Lagrangian outside of inclusions is shown to have the same form as the
Einstein-Hilbert Lagrangian for free space. Properties of the fabric such as
strain, stress, vibrations, and elastic moduli are related to properties of
gravity and space, such as the gravitational potential, gravitational
acceleration, gravitational waves, and the energy density of free space. By
introducing a mechanical analogy of General Relativity, we enable the
application of Solid Mechanics tools to address problems in Cosmology.
