Segmentation of lungs with large tumors is a challenging and time-consuming task, especially for 4D CT data sets used in radiation therapy. Existing lung segmentation methods are ineffective in these cases, because they are either not able to deal with large tumors and/or process every 3D image independently neglecting temporal information. In this paper, we present a approach for model-based 4D segmentation of lungs with large tumors in 4D CT data sets. In our approach, a 4D statistical shape model that accounts for inter- and intra-patient variability is fitted to the 4D image sequence, and the segmentation result is refined by a 4D graph-based optimal surface finding. The approach is evaluated using 10 4D CT data sets of lung tumor patients. The segmentation results are compared with a standard intensity-based approach and a 3D version of the presented model-based segmentation method. The intensity-based approach shows a better performance for normal lungs, however, fails in presence of large lung tumors. Although overall performance of 3D and 4D model-based segmentation is similar, the results indicate improved temporal coherence and improved robustness with respect to the segmentation parameters for the 4D model-based segmentation.