A bstract The ATLAS experiment at the LHC has measured the production cross section of events with two isolated photons in the final state, in proton-proton collisions at $ \sqrt{s}=7\;\mathrm{TeV} $ . The full data set collected in 2011, corresponding to an integrated luminosity of 4 . 9 fb −1 , is used. The amount of background, from hadronic jets and isolated electrons, is estimated with data-driven techniques and subtracted. The total cross section, for two isolated photons with transverse energies above 25 GeV and 22 GeV respectively, in the acceptance of the electromagnetic calorimeter (| η | < 1 . 37 and 1 . 52 < | η | < 2 . 37) and with an angular separation Δ R > 0 . 4, is $ 44.0_{-4.2}^{+3.2 } $ pb. The differential cross sections as a function of the di-photon invariant mass, transverse momentum, azimuthal separation, and cosine of the polar angle of the largest transverse energy photon in the Collins-Soper di-photon rest frame are also measured. The results are compared to the prediction of leading-order parton-shower and next-to-leading-order and next-to-next-to-leading-order parton-level generators.