A damage detection and assessment algorithm is developed based on system identification using a finite element model and the measured modal response of a structure. The measurements are assumed to be sparse and polluted with noise. A change in an element constitutive property from a baseline value is taken as indicative of damage. An adaptive parameter grouping updating scheme is proposed to localize the damage zones in the structure and a Monte Carlo method is used with a data perturbation scheme to provide a statistical basis for assessing damage. Damage indices computed from the Monte Carlo sample of data perturbations are used to assess damage. The threshold values, which distinguish damage from measurement noise, are established through Monte Carlo simulation on the baseline structure. The proposed algorithm is applied to the problem of locating a crack in a cantilever beam. A Bernoulli-Euler beam model and a plane stress model are employed to illustrate the use of the method and compare the efficacy of the two models for crack detection.