  The accurate determination of cluster total mass is crucial for their use as
probes of cosmology. Recently, the Sunyaev--Zel'dovich effect (SZE) has been
exploited in surveys to find galaxy clusters, but X-ray or lensing follow up
observations, or empirically-determined scaling relations between SZE flux and
total mass, have been required to estimate their masses. Here we demonstrate a
new method of mass determination from SZE observations, applicable in the
absence of X-ray or lensing data. This method relies on the virial relation and
a minimal set of assumptions, following an approach analogous to that used for
stellar structure. By exploiting the virial relation, we implicitly incorporate
an additional constraint from thermodynamics that is not used in deriving the
equation of hydrostatic equilibrium. This allows us to relate cluster total
mass directly to the robustly-determined quantity, the integrated SZE flux.
