  We find the classical supersymmetric vacuum states of a class of N = 1* field
theories obtained by mass deforming superconformal models with simple gauge
groups and N = 4 or N =2 supersymmetry. In particular, new classical vacuum
states for mass-deformed N = 4 models with Sp(2N) and SO(N) gauge symmetry are
found. We also derive the classical vacua for various mass-deformed N=2 models
with Sp(2N) and SU(N) gauge groups and antisymmetric (and symmetric)
hypermultiplets. We suggest interpretations of the mass-deformed vacua in terms
of three-branes expanded into five-brane configurations.
