Relativistic configuration interaction calculations are done for Kr ions Kr II and Kr III. Transition energies and transition probabilities for 122 transitions between Kr II 4p5J = 1/2, 3/2→ 1s 4p6, 1s 4p5np (n = 5–8) J = 1/2, 3/2, 5/2; 437 transitions between Kr III 4p4J = 0, 1, 2→ 1s 4p5, 1s 4p4np (n = 5–8) J = 0, 1, 2, 3 have been calculated. These data have been used by experiment to reproduce the absorption spectrum of Kr II and Kr III and found to be in good agreement with their measurement. Also, the K-edge energy of neutral Kr, Kr II and Kr III has been calculated. The first is within 0.94 eV of an existing experiment, while the last two are calculated for the first time.