Model systems of the tryptophan radical, present in several biological systems such as DNA photolyase, cytochrome c peroxidase, and mutated ribonucleotide reductase, have been investigated using gradient-corrected density functional theory (DFT). We report calculated spin densities and complete hyperfine tensors for all atoms, as well as potential energy and P-proton hyperfine tensor curves for the rotation about the C3-C beta bond. Effects of hydrogen bonding to the N1 nitrogen (neutral radical) or N1-H hydrogen (cationic radical) are investigated, as is the C3 dioxygen adduct (peroxide) radical. Throughout comparisons are made to experimental data and previous theoretical studies of tryptophan model systems. The calculations support the earlier assignments of neutral Trp radicals present in mutant Y122F Escherichia coli ribonucleotide reductase at low temperatures, but most likely charged radical cations in DNA photolyase and yeast cytochrome c peroxidase. Although the calculations give clear-cut answers to, for example, the geometric arrangements, they are unable to resolve all of the ambiguities regarding the Trp radicals in the above systems, primarily due to lack of sufficient well-resolved data to compare with.