A two-phase geometric and analytical modeling method is presented to model long needle insertion in deformable bio-tissues. Analytical modeling and computational algorithms are also introduced to evaluate different geometric needle design for biomedical applications. Needle insertion techniques have great potential to improve medical procedures, such as various cancer treatments, including brachytherapy, drug delivery, local cell treatment, biosampling, and the controlled release of medicine. During medical treatment procedures of long needle insertion, needle bending or buckling may occur, causing unpredictable needle placement and motion, as well as excessive damage to the surrounding tissues. Analytical and geometric modeling techniques are developed based on the interaction forces between the needle and the soft and hard tissues to better model the needle bending and buckling during insertion into bio-tissues. Multiple parameters such as various bevel tip angles and variant needle materials are studied. Additionally, a haptic-based human-computer interface with force and torque feedback is developed. The techniques presented in this paper can ultimately be used to better the design and manufacturing of biomedical applications.