Abstract: To locate structural damages for differently supported beams, one method of flexibility curvature M_FC was constructed by the maximum in each column of flexibility matrix for cantilever beams. The other method of flexibility curvature D_FC was constructed from principal diagonal elements of flexibility matrix as a new indicator for non-cantilever beams. The numerical simulation sups indicate that the damage location in structures can be identified without baseline modal parameters by D_FC for non-cantilever beams and M_FC for cantilever beams, by which not only simple damage but also multiple ones can be detected and degree of structural damage can also be derived by using only a few of the lower frequency modes.