  We study fine properties of L\'evy trees that are random compact metric
spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous
state branching processes. L\'evy trees are the scaling limits of Galton-Watson
trees and they generalize Aldous's continuum random tree which corresponds to
the Brownian case. In this paper we prove that L\'evy trees have always an
exact packing measure: We explicitely compute the packing gauge function and we
prove that the corresponding packing measure coincides with the mass measure up
to a multiplicative constant.
