  We study analytically the medium-induced energy loss of a high energy parton
passing through a finite size QCD plasma, which is expanding longitudinally
according to Bjorken's model. We extend the BDMPS formalism already applied to
static media to the case of a quark which hits successive layers of matter of
decreasing temperature, and we show that the resulting radiative energy loss
can be as large as 6 times the corresponding one in a static plasma at the
reference temperature $T = T (L)$, which is reached after the quark propagates
a distance $L$.
