The modeling of respiratory motion is important for a more accurate understanding and accounting of its effect on dose to cancers in the thorax and abdomen by radiotherapy. We have developed a model of respiration-induced organ motion in the thorax without the commonly adopted assumption of repeatable breath cycles. The model describes the motion of a volume of interest within the patient based on a reference three-dimensional (3D) image (at end expiration) and the diaphragm positions at different time points. The input data are respiration-correlated CT (RCCT) images of patients treated for non-small- cell lung cancer, consisting of 3D images, including the diaphragm positions, at ten phases of the respiratory cycle. A deformable image registration algorithm calculates the deformation field that maps each 3D image to the reference 3D image. A principal component analysis is performed to parameterize the 3D deformation field in terms of the diaphragm motion. We show that the first two principal components are adequate to accurately and completely describe the organ motion in the data of four patients. Artifacts in the RCCT images that commonly occur at the mid-respiration states are reduced in the model-generated images. Further validation of the model is demonstrated in the successful application of the parameterized 3D deformation field to RCCT data of the same patient but acquired several days later. We have developed a method for predicting respiration-induced organ motion in patients that has potential for improving the accuracy of dose calculation in radiotherapy. Possible limitations of the model are cases where the correlation between lung tumor and diaphragm position is less reliable such as superiorly situated tumors and interfraction changes in tumor-diaphragm correlation. The limited number of clinical cases examined suggests, but does not confirm, the model's applicability to a wide range of patients.