  We describe a strategy for a non-perturbative computation of the b-quark mass
to leading order in 1/m in the Heavy Quark Effective Theory (HQET). The
approach avoids the perturbative subtraction of power law divergencies, and the
continuum limit may be taken. First numerical results in the quenched
approximation demonstrate the potential of the method with a preliminary result
m_b(4GeV)=4.56(2)(7) GeV. In principle, the idea may also be applied to the
matching of composite operators or the computation of 1/m corrections in HQET.
