Lung radiotherapy is greatly benefitted when the tumor motion caused by breathing can be modeled. The aim of this paper is to present the importance of using anisotropic and subject-specific tissue elasticity for simulating the airflow inside the lungs. A computational-fluid-dynamics (CFD) based approach is presented to simulate airflow inside a subject-specific deformable lung for modeling lung tumor motion and the motion of the surrounding tissues during radiotherapy. A flow-structure interaction technique is employed that simultaneously models airflow and lung deformation. The lung is modeled as a poroelastic medium with subject-specific anisotropic poroelastic properties on a geometry, which was reconstructed from four-dimensional computed tomography (4DCT) scan datasets of humans with lung cancer. The results include the 3D anisotropic lung deformation for known airflow pattern inside the lungs. The effects of anisotropy are also presented on both the spatiotemporal volumetric lung displacement and the regional lung hysteresis.