  The compatibility conditions for generalised continua are studied in the
framework of differential geometry, in particular Riemann-Cartan geometry. We
show that Vall\'{e}e's compatibility condition in linear elasticity theory is
equivalent to the vanishing of the three dimensional Einstein tensor. Moreover,
we show that the compatibility condition satisfied by Nye's tensor also arises
from the three dimensional Einstein tensor which appears to play a pivotal role
in continuum mechanics not mentioned before. We discuss further compatibility
conditions which can be obtained using our geometrical approach and apply it to
the micro-continuum theories.
