  We describe the asymptotic behaviour of a cylindrical elastic body,
reinforced along identical $\epsilon$-periodically distributed fibers of size
$r_{\epsilon}$, with $0 < r_{\epsilon} < \epsilon$, filled in with some
different elastic material, when this small parameter $\epsilon$ goes to 0. The
case of small deformations and small strains is considered. We exhibit a
critical size of the fibers and a critical link between the radius of the
fibers and the size of the Lam\'e coefficients of the reinforcing elastic
material. Epi-convergence arguments are used in order to prove this asymptotic
behaviour. The proof is essentially based on the construction of appropriate
test-functions.
