  N-body + hydrodynamic simulations of galaxy clusters are used to demonstrate
a correlation between galaxy cluster mass and the strength of the
Sunyaev-Zel'dovich (SZ) effect induced by the cluster. The intrinsic scatter in
the correlaton is larger than seen in the cluster mass -- X-ray temperature
correlation, but smaller than seen in the correlation between mass (or
temperature) and X-ray luminosity, as expected. Using the convergence to
self-similarity of cluster structure at larger radii, a simple area-averaged SZ
value derived from mock SZ maps also correlates well with mass; the intrinsic
scatter in this correlation is comparable to that seen in simulations for the
mass -- temperature correlation. Such a relation may prove a powerful tool for
estimating cluster masses at higher redshifts.
