Viscoelasticity of the spinal nerve roots may play a significant role in predicting nerve root damage caused by overall spinal motion. However, only a few studies have investigated the complex mechanical behavior of this tissue. The current study presents a theoretical protocol for predicting mechanical responses of soft biological materials, and this method was used to a uniaxially stretched neural fiber bundle isolated from porcine spinal nerve roots with various loading configurations. Stress relaxation tests were performed to systematically determine a set of parameters dictating the stress decaying process, i.e., a set of relaxation moduli and the corresponding time constants. Based on the obtained experimental and numerical test data, it was confirmed that the proposed method is effective even for the prediction of mechanical response to a cyclic stretch immediately after the ramp-hold test. In addition, an elastic response, i.e., a stress–strain relationship under a high-rate loading regime, was determined analytically. The results demonstrated that instantaneous mechanical responses of neural fiber bundles can be stiffened against very rapid stretch (>10 s−1); however, the fibers are relatively insensitive to moderate loading rates (<1 s−1). The ultimate tensile strength was estimated to be approximately 8 MPa at the structural failure strain (15%). This information will enable the computational assessment of traumatic nerve root injuries sustained during traffic accidents and contact sports.