This study employs genetic algorithms to solve clustering problems. Three models, SICM, STCM, CSPM, are developed according to different coding/decoding techniques. The effectiveness and efficiency of these models under varying problem sizes are analyzed in comparison to a conventional statistics clustering method (the agglomerative hierarchical clustering method). The results for small scale problems (10-50 objects) indicate that CSPM is the most effective but least efficient method, STCM is second most effective and efficient, SICM is least effective because of its long chromosome. The results for medium-to-large scale problems (50-200 objects) indicate that CSPM is still the most effective method. Furthermore, we have applied CSPM to solve an exemplified p-Median problem. The good results demonstrate that CSPM is usefully applicable.