  The medium induced energy loss spectrum of a high energy quark or gluon
traversing a hot QCD medium of finite volume is studied. We model the
interaction by a simple picture of static scattering centres. The total induced
energy loss is found to grow as $L^2$, where $L$ is the extent of the medium.
The solution of the energy loss problem is reduced to the solution of a
Schr\"odinger-like equation whose ``potential'' is given by the
single-scattering cross section of the high energy parton in the medium. These
resuls should be directly applicable to a quark-gluon plasma.
