The measurement of the elastic properties of human tissue, or elastography, allows for the quantitative assessment of tissue functionality. Patients undergoing radiation therapy often present with lung disease, such as COPD, which is known to cause degradation of tissue elasticity. The reliance of normal lung function on these elastic properties is well established, underscoring the importance of function-preserving efforts in radiotherapy. Regional elasticity distributions may be used to identify regions of parenchymal tissue that contribute significantly to lung function. This knowledge can, in turn, aid in functional lung sparing efforts during the treatment planning process. Previous elastography efforts have been performed using a well-validated biomechanical model in combination with model-based CT images. Recent studies also suggest that biomechanical modeling and elasticity estimation may prove to have useful applications outside of the radiotherapy domain. These tools could potentially help improve the evaluation of patient candidacy and outcome prediction for various lung interventions, such as lung volume reduction surgery (LVRS) or bronchoscopic lung volume reduction (BLVR) procedures. The first aim of the dissertation was to develop and improve current CT-based elastography algorithms and tools. This aim was addressed by carrying out a consistency study where elastography was performed using separate image datasets generated from scans acquired at different points in the breathing trace for each patient. As part of a feasibility study to test the hypothesis that additional elasticity information could be obtained using large deformation image pairs, an elastography method was developed for use with breath-hold CT images acquired at the forced breathing stages of residual volume (RV) and total lung capacity (TLC). The second aim was to investigate the applications of biomechanical modeling and elastography for other function-preserving treatment interventions. This work involved the development of a quorum-based machine learning approach to perform lobar segmentation for lobe identification in lung intervention simulations and lobe-wise analyses. A framework for simulating a lobectomy procedure by incorporating elasticity information and biomechanical modeling was also constructed. Using this framework, the feasibility of using the resulting predicted post-intervention lung geometry for approximating pulmonary function test (PFT) values was investigated. The third aim of this proposal was to develop and employ a machine learning application for elasticity estimation from single end-exhalation breath-hold CT scans. A conditional generative adversarial (cGAN) neural network was built and validated for elasticity estimation. We further investigated the effects of the imaging dose used during the acquisition of CT image data on the accuracy of the proposed machine learning implementation. The expanded use of biomechanical modeling and elastography within the radiotherapy context has the potential to improve functional avoidance efforts for patients presenting with co-morbidities affecting lung function prior to treatment. Additionally, there is an opportunity to extend these tools toward improving and informing other lung intervention efforts. Finally, the ability to take advantage of CT-based elastography methods through machine learning in scenarios where model-based CT is not typically available could expand the scope of CT-based elastography in both the radiotherapy domain and for the expanded use in other lung intervention workflows. The tools and applications presented in this dissertation aim to highlight and expand the benefits of CT-based biomechanical modeling and elastography within the radiotherapy domain and for use with other lung intervention procedures.