New constraints on supergravity models from b --> s$\gamma$

We perform a detailed study of the constraints from b\to s\gamma on a large class of supergravity models, including generic four-parameter supergravity models, the minimal SU(5) supergravity model, and SU(5)\times U(1) supergravity. For each point in the parameter spaces of these models we obtain a range of B(b\to s\gamma) values which should conservatively account for the unknown next-to-leading-order QCD corrections. We then classify these points into three categories: ``excluded" points have ranges of B(b\to s\gamma) which do not overlap with the experimentally allowed range, ``preferred" points have B(b\to s\gamma) ranges which overlap with the Standard Model prediction, and ``Ok" points are neither ``excluded" nor ``preferred" but may become ``excluded" should new CLEO data be consistent with the Standard Model prediction. In {\em all} cases we observe a strong tendency for the ``preferred" points towards one sign of the Higgs mixing parameter \mu. For the opposite sign of \mu there is an upper bound on \tan\beta: \tan\beta\lsim25 in general, and \tan\beta\lsim6 for the ``preferred" points. We conclude that new CLEO data will provide a decisive test of supergravity models.