  We present novel Monte Carlo methods for treating the interacting shell model
that allow exact calculations much larger than those heretofore possible. The
two-body interaction is linearized by an auxiliary field; Monte Carlo
evaluation of the resulting functional integral gives ground-state or thermal
expectation values of few-body operators. The ``sign problem'' generic to
quantum Monte Carlo calculations is absent in a number of cases. We discuss the
favorable scaling of these methods with nucleon numb er and basis size and
their suitability to parallel computation.
