  The redshift dependence of the observed cluster abundance due to the
Sunyaev-Zeldovich Effect (SZE) is studied in various cosmological models
including flat and open homogeneous (CDM) models and an inhomogeneous model
with a large-scale local void. The Press-Schechter formalism is used to derive
the abundance at epochs 0 < z < 2 and the cluster mass limit Mlim is given from
a flux limit for SZE. It is shown that SZE is useful for constraining the
cosmological model parameters, and the abundance in the inhomogeneous model may
be comparable with that in the low-density homogeneous models. The significance
of relative difference of abundances in the various models is discussed.
