The determination of the weights of the influencing factors in evaluating the suitability of engineering sites varies greatly among the conventional methods which are generally found unreliable when applied to some engineering sites with complex geology for their failure to reveal the complex relationships between the geological factors. To satisfy the need of selecting proper sites for large-scale key projects, we improve the constant weight to variety weight and introduce the matrix of multifactor interactions into the suitability evaluation of engineering sites, and propose the concept of engineering site suitability index (ESSI), a comprehensive index which is capable of considering the correlations between the influencing factors and the variation of their impact under various tamporospatial dimensions; and therefore put forward a multi-discipline system for evaluating the suitability of engineering sites. The system is used in the site selection for China Spallation Neutron Source(CSNC) Project, and found applicable and reliable by the follow-up engineering investigation. The ESSI system which is based on the matrix of multi-factor interactions is proved scientific, reasonable, and applicable by case studies; and it is expected to provide a reference for similar large-scale engineering