Continuum robots actuated by tendons are a widely researched robot design offering high dexterity and large workspaces relative to their volume. Their flexible and compliant structure can be easily miniaturized, making them predestined for applications in difficult-to-reach and confined spaces. Adaption of this specific robot design includes extensible segments leading to an even higher manipulability and enabling so-called follow-the-leader motions of the manipulator. In this letter, kinematic modeling for a tendon actuated continuum robot with three extensible segments is investigated. The focus is drawn on the comparison of two of the most widely used modeling approaches both for freespace and loaded configurations. Through extensive experimental validation, the modeling performances are assessed qualitatively and quantitatively in terms of the shape deviation, Euclidean error at segment ends, and computation time. While Cosserat rod modeling is slightly more accurate than beam mechanics modeling, the latter presents significantly lower computation time.