The well-known Kolosov–Muskhelishvili (KM) representation of the Airy function for 2D stress analysis in complex variable terms is enhanced by combining it with Walsh wavelets decomposition. It allows us to perform general analytical derivations up to the maximum extent possible which, in turn, provides a basis for developing a new stress computation algorithm readily incorporated into the routine single scale KM scheme. The mathematical treatment of the wavelet application is supported by a number of examples where non-trivial closed-form solutions are known and serve as a benchmark for numerical simulations. The comparison shows that the proposed framework has better performance than the conventional Fourier transform, especially when it comes to non-smooth stress distributions.