Computational models for tethers, chains, and ropes are prevalent in mechanical and aerospace systems. Many different model structures, spanning multiple applications, appear in the literature; however, little work exists to show how these different models compare with respect to accuracy, computational expense, and numerical reliability. In this work three discrete tether models, a recursive multi-body model, a Kelvin-Voigt visco-elastic model, and a Standard Linear visco-elastic model, are all compared. Comparisons of each model are made with experimental data collected for tethers of varying material, physical properties, and loading conditions resulting in substantial nonlinear effects. Results show that each model, depending in the application and expected loading, has advantages and disadvantages in regard to computational burden, accuracy, and numerical stability. Guidelines based on the results provide suggestions to which tether models may be most appropriate for a variety of applications. [ABSTRACT FROM AUTHOR]