Standardized testing methods for the mechanical characterization of biological soft tissues remain underdeveloped in several domains. Existing clamping methods often induce high stress levels in the clamping region, thereby affecting experimental outcomes. This study introduces a 3D-printed clamping system based on the capstan principle. The capstan system was designed and manufactured using 3D printing technology and optimized to minimize the required gripping pressure while maintaining the natural, non-tapered state of specimens. This optimization helps reduce experimental artifacts and prevents premature tissue failure in the clamping region caused by local stress peaks. Usability trials were conducted using human flexor digitorum profundus (FDP) tendons (n = 15). Results showed that 80% of the tendons failed at the midpoint region, indicating the desired load distribution achieved by the clamping mechanism. The elastic moduli, averaging 316.18 ± 86.73 MPa, and failure load properties, averaging 79.25 ± 19.10 MPa, fell within the range of FDP values reported by other researchers, thereby supporting the validity of the capstan design. Capstan clamping offers a promising add-on for biomechanical testing of soft tissues. Further development is necessary to tailor the clamping design to various tissue geometries and to address issues related to tissue moisture regulation, thereby enhancing the reliability and versatility of the clamping system.