Many multi-story or highrise buildings consisting of a number of identical stories are usually considered as periodic spring-mass systems. The general expressions of natural frequencies, mode shapes, slopes and curvatures of mode shapes of periodic spring-mass system by utilizing the periodic structure theory are derived in the paper, moreover, the sensitivities of these mode parameters with respect to structural damages, which do not depend on physical parameters of the original structures, are obtained. Based on the sensitivity analysis of these mode parameters, a two-stage method is proposed to localize and quantify damages of multi-story or highrise buildings. The slopes and curvatures of mode shapes, which are highly sensitive to local damages, are used to localize the damages, subsequently, the limited measured natural frequencies, which have a better accuracy than the other mode parameters, are used to quantify the extent of damages within the potential damaged locations. The experimental results of a 3-storey experimental building demonstrate that the single or multiple damages of buildings, either slight or severe, can be correctly localized by using only the slope or curvature of mode shape in one of the lower modes, in which the change of natural frequency is the largest, and can be accurately quantified by the limited measured natural frequencies with noise pollution.