Identification, localization and quantification of structural damage can be performed through a model-updating procedure. Model-updating methods require a baseline finite element (FE) model of the undamaged structure, which imposes a restriction on their applicability and can become very problematic especially for large and complex civil structures. Modeling errors in the baseline model whose effects exceed the modal sensitivity to damage are critical and make an accurate estimation of damage impossible. This paper presents an identification algorithm using modal data for assessing structural damage that is based on FE-updating procedures and takes modeling error into account. To overcome its influence, differences of mode shapes and frequencies before and after damage for both numerical model and experimental measurements are used instead of the mode shapes and frequencies themselves. To formulate the objective function, two different approaches have been considered taking into account how these differences are grouped: a single-objective approach and a multiobjective approach. The effectiveness of both approaches is verified against numerical and experimental results.