In this talk, the diagrams of affine permutations and their balanced labellings will be introduced. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, it turned out the sum of weight monomials of the column strict balanced labellings is the affine Stanley symmetric function defined by Lam. The affine Stanley symmetric function is the affine counterpart of the Stanley symmetric function which plays an important role in Schubert calculus. Our construction is a natural tableau-theoretic realization of this function. We also give a necessary and sufficient condition for a cylindric diagram to be an affine permutation diagram. This talk is based on the joint work with Taedong Yun.