Umbilical Cord Accidents (UCA) are a common birth complication that results in the deaths of 2 out every 1000 normal babies [4]. Because mechanical properties directly play a role in the response of the cord to deformation, understanding these properties is necessary to develop a structural model of the cord that could be used to predict UCA susceptibility. To validate testing and modeling procedures, the stress relaxation response of an equine umbilical vein and artery were fit to a model based on YC Fung's Quasilinear Viscoelastic (QLV) theory. Upon comparison, the model successfully reproduced the experimental stress relaxation response. Longitudinal stress relaxation and stress/strain tests were performed on samples of human umbilical artery, keeping track of their location in reference to the placenta to determine whether mechanical properties varied based on location. Parameters for the QLV model were derived from the stress relaxation test, but although there were differences based on location, the sample number (n=3) per group was too small to develop conclusions. The relaxation in each sample proceeded more rapidly and for a much longer time than data published for canine arteries. These results provided a stepping stone for future work. Final stress relaxation experiments were run on the fetal (n = 9), placental (n = 8), and middle (n=7) sections of human umbilical cords. Time-dependent QLV parameters were extracted from the hold section of the stress relaxation. The curve-fitting procedure was performed by the Matlab curve-fitting tool. Statistical analysis demonstrated that there were no differences between sections, with one exception. At the placental end, relaxation was initiated more quickly than in the other sections: a possible defense mechanism for rapid fetal movements. In each of the three sections, relaxation proceeded for an extended period of time (on the order of 10,000 seconds) in comparison to typical adult arteries (on the order of 600 seconds). From the ramp section of the stress relaxation test, stress/strain properties were investigated. Again, statistical analysis demonstrated that there were no differences between sections. While conclusions can be drawn from this work, much is still unknown about the function of the umbilical cord.