Silicone nerve cuff electrodes are commonly implanted on relatively large and accessible somatic nerves as peripheral neural interfaces. While these cuff electrodes are soft (1-50 MPa), their self-closing mechanism requires of thick walls (200-600 µm), which in turn contribute to fibrotic tissue growth around and inside the device, compromising the neural interface. We report the use of thiol-ene/acrylate shape memory polymer (SMP) for the fabrication of thin film multi-electrode softening cuffs (MSC). We fabricated multi-size MSC with eight titanium nitride (TiN) electrodes ranging from 1.35 to 13.95 × 10-4 cm2 (1-3 kΩ) and eight smaller gold (Au) electrodes (3.3 × 10-5 cm2; 750 kΩ), that soften at physiological conditions to a modulus of 550 MPa. While the SMP material is not as soft as silicone, the flexural forces of the SMP cuff are about 70-700 times lower in the MSC devices due to the 30 μm thick film compared to the 600 μm thick walls of the silicone cuffs. We demonstrated the efficacy of the MSC to record neural signals from rat sciatic and pelvic nerves (1000 µm and 200 µm diameter, respectively), and the selective fascicular stimulation by current steering. When implanted side-by-side and histologically compared 30 days thereafter, the MSC devices showed significantly less inflammation, indicated by a 70-80% reduction in ED1 positive macrophages, and 54-56% less fibrotic vimentin immunoreactivity. Together, the data supports the use of MSC as compliant and adaptable technology for the interfacing of somatic and autonomic peripheral nerves.