In this paper, we present the implementation of a small library of three-dimensional cohesive elements. The elements are formatted as user-defined elements, for compatibility with the commercial finite element software ABAQUS. The PPR, potential-based traction-separation relation is chosen to describe the element’s constitutive model. The intrinsic cohesive formulation is outlined due to its compatibility with the standard, implicit finite element framework present in ABAQUS. The implementation of the cohesive elements is described, along with instructions on how to incorporate the elements into a finite element mesh. Specific areas of the user-defined elements, in which the user may wish to modify the code to meet specific research needs, are highlighted. Numerical examples are provided which display the capabilities of the elements in both small deformation and finite deformation regimes. A sample element source code is provided in an Appendix, and the source codes of the elements are supplied through the website of the research group of the authors.