************************************************************************* 71166 The cluster mass function and its evolutionary effect is the best measure to investigate the structure formation history of the universe. However, the observational study of the cluster evolution has so far been performed mainly in terms of the X-ray luminosities, which is indirect and subject to systematic errors. In order to obtain a tight constraint on the cosmological models, we are aiming to construct the cluster mass function in the medium redshift universe of z=0.2-0.3 with much less uncertainties. For this purpose, we compiled a flux-limited complete sample from the ROSAT All Sky Survey data, which consists of eight clusters. The ASCA observation of the three clusters proposed here will complete the mass measurements of our sample clusters. *************************************************************************