Damage assessments of concrete structures are essential to determine their seismic performances under earthquake events. In this paper, six three bays two dimensional concrete frames, five to ten story high, were analyzed under 30 near-field earthquake records by nonlinear dynamic analyses. The seismic performances were evaluated using two important overall damage indices which are: the modified Park-Ang index and the maximum softening damage index. The correlations between several seismic parameters and the two damage indices of the six concrete frames were determined using Spearman correlation coefficient. In the end, the values of correlations between seismic parameters and these two damage indices were compared and discussed. Subsequently, seismic parameters that have the strongest and the fairest correlation were presented. The numerical results of correlations have shown that Velocity Spectrum Intensity (VSI) has a strong interdependency with two overall structural damage indices (the modified Park-Ang model and the maximum softening damage) for all of the reinforced concrete frames.