Diagnosis and therapy planning in oncology applications often rely on the joint exploitation of two complementary imaging modalities, namely Computerized Tomography (CT) and Positron Emission Tomography (PET). While recent technical advances in combined CT/PET scanners enable 3D CT and PET data of the thoracic region to be obtained with the patient in the same global position, current image data registration methods do not account for breathing-induced anatomical changes in the thoracic region, and this remains an important limitation. This paper deals with the 3D registration of CT thoracic image volumes acquired at two different instances in the breathing cycle and PET volumes of thoracic regions. To guarantee physiologically plausible deformations, we present a novel method for incorporating a breathing model in a non-linear registration procedure. The approach is based on simulating intermediate lung shapes between the two 3D lung surfaces segmented on the CT volumes and finding the one most resembling the lung surface segmented on the PET data. To compare lung surfaces, a shape registration method is used, aligning anatomical landmark points that are automatically selected on the basis of local surface curvature. PET image data are then deformed to match one of the CT data sets based on the deformation field provided by surface matching and surface deformation across the breathing cycle. For pathological cases with lung tumors, specific rigidity constraints in the deformation process are included to preserve the shape of the tumor while guaranteeing a continuous deformation.