We present simulations of the cluster distribution in several dark matter models, using an optimized version of the truncated Zeldovich approximation (TZA). We compare them with N-body cluster simulations and find that the TZA provides a very accurate description of the cluster distribution as long as fluctuations on the cluster mass scale are in the mildly non-linear regime. The simulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) with n=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant (h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with Omega_0=0.2. We compare the simulations with a redshift sample of Abell/ACO clusters, using the integral of the 2-point correlation function and the probability density function. We find that the best models at reproducing the data are CHDM and LCDM. All the other models are ruled out. The reduced skewness S_3 is fairly constant with S_3=1.9, independent of the DM model and consistent with observational data. The abundances of clusters predicted using the Press--Schechter theory provide strong constraints: only the CHDM, LOWH and LCDM models appear to produce the correct number-density of clusters.
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