Transverse compression tests are the established way to identify the transverse mechanical properties of single fibers. However, to the authors knowledge, the influence of an angle between the two compression platens has never been studied or quantified. In this paper, the importance of platen parallelism is studied for the first time through: numerical simulation and experimental investigation. A sensitivity analysis complements these studies by highlighting the importance of contact geometry in the analytical model, used in the inverse identification of the fiber’s apparent transverse elastic modulus ET . Experimental results show that a misalignment of 1◦ between the platens produces a variation of more than 35% on the identified ET , compared to a compression with parallel platens. Given the importance of platen misalignment angle an experimental setup and protocol are designed in order to maintain this angle below 0.1◦, thus keeping the error on ET below 5%