Despite the significant advantages of Shape Memory Polymers (SMPs), material processing and production challenges have limited their applications. Recent advances in fiber manufacturing offer a novel approach to processing polymers, broadening the functions of fibers beyond optical applications. In this study, a thermal drawing technique for SMPs to fabricate Shape Memory Polymer Fibers (SMPFs) tailored for medical applications, featuring programmable stiffness and shape control is developed. Rheological and differential scanning calorimetry analyses are conducted to assess SMP's compatibility with the proposed thermal drawing process and applications, leading to the production of multilumen, multimaterial SMPFs activated at body temperature. Different properties of SMPFs are investigated in three medical devices: stiffness-adjustable catheters, softening neural interface, and shape-programmable cochlear implants. Comprehensive characterization of these devices demonstrates the potential of thermally drawn SMPs to be employed in a wide range of applications demanding programmable mechanical properties.