We analyze the Krawtchouk polynomials K n (x, N, p, q) asymptotically. We use singular perturbation methods to analyze them for N → ∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0, N ] × [0, N ], involving some special functions. We give numerical examples showing the accuracy of our formulas.