  We present and modernize Souriau's 1958 geometric framework for Relativistic
continuous media, and enlighten the necessary and the ad hoc modeling choices
made since, focusing as much as possible on the Continuum Mechanics point of
view. We describe the general covariant formulation of Hyperelasticity in
General Relativity, and then in the particular case of a static spacetime.
Finally, we apply this formalism for the Schwarzschild's metric, and recover
the Classical Galilean Hyperelasticity with gravity, as the Newton-Cartan
infinite light speed limit of this formulation.
