Separation of the radioisotope 85Kr from 136Xe is an important target during used nuclear fuel recycling. We report a detailed study on the Kr and Xe adsorption, diffusion, and membrane permeation properties of the silicoaluminophosphate zeolite SAPO‐34. Adsorption and diffusion measurements on SAPO‐34 crystals indicate their potential for use in Kr‐Xe separation membranes, but also highlight competing effects of adsorption and diffusion selectivity. SAPO‐34 membranes are synthesized on α−alumina disk and tubular substrates via steam assisted conversion seeding and hydrothermal growth, and are characterized in detail. Membrane transport measurements reveal that SAPO‐34 membranes can separate Kr from Xe by molecular sieving, with Kr permeabilities around 50 Barrer and mixture selectivity of 25–30 for Kr at ambient or slight sub‐ambient conditions. The membrane transport characteristics are modeled by the Maxwell‐Stefan equations, whose predictions are in very good agreement with experiment and confirm the minimal competing effects of adsorption and diffusion. © 2016 American Institute of Chemical Engineers AIChE J, 63: 761–769, 2017