To propose more useful strong motion indices and to improve estimation accuracy of building damage, some strong motion indices (peak ground velocity, spectrum intensity, Japan Meteorological Agency seismic intensity, spectral displacement, etc.) are investigated with respect to correlation with damage of wooden structures. A nonparametric correlation coefficient, Spearman's Ρ, is employed as an indicator of accuracy of damage estimation. Multiple input motions are used for nonlinear time history analysis of two-degree-of-freedom models of wooden structures, which have various combinations of story stiffnesses. As a damage model, maximum story drift angle is considered and three levels of threshold, 1/60, 1/30 and 1/15 rad are examined, which approximately correspond to minor, moderate, and major damage of a structure. Distributions of Spearman's Ρof the strong motion indices are compared, and it is revealed that displacement response of a linear single-degree-of-freedom system with a damping ratio of 20% and with the elongated period that is determined by a damage threshold, shows fairly good correlation with the structural damage.