We interpret the UV absorption and fluorescence of cysteine and cystine from ab initio calculations of the ground states and lowest excited singlet states of the two molecules. We derive the optimized energies and geometry parameters from HF/6-31G computations on the ground state and CIS/6-31G computations of the excited state. We present vibrational frequencies of the ground and excited states and quantitative predictions for UV absorption and fluorescence. We also show experimental measurements of cystine fluorescence. Cystine is shown to fluoresce at 700 nm.