  The paper presents a reformulation of some of the most basic entities and
equations of linear elasticity - the stress and strain tensor, the Cauchy
Navier equilibrium equations, material equations for linear isotropic bodies -
in a modern differential geometric language using differential forms and lie
derivatives. Similar steps have been done successfully in general relativity,
quantum physics and electrodynamics and are of great use in those fields. In
Elasticity Theory, however, such a modern differential geometric approach is
much less common. Furthermore, existing reformulations demand a vast knowledge
of differential geometry, including nonstandard entities such as vector valued
differential forms and the like. This paper presents a less general but more
easily accessible approach to using modern differential geometry in elasticity
theory than those published up to now.
