  Relativistic elasticity on an arbitrary spacetime is formulated as a
Lagrangian field theory which is covariant under spacetime diffeomorphisms.
This theory is the relativistic version of classical elasticity in the
hyperelastic, materially frame-indifferent case and, on Minkowski space,
reduces to the latter in the non-relativistic limit . The field equations are
cast into a first -- order symmetric hyperbolic system. As a consequence one
obtains local--in--time existence and uniqueness theorems under various
circumstances.
