This paper studies sound propagation in a layered atmosphere bounded by a ground, whose impedance is described by the Delany–Bazley–Chessell’s empirical model. The problem is formulated in terms of a Green’s function integral in the spectral domain, and is numerically evaluated by a Fast Field Program (FFP). Numerical results are included to show that (i) in simple test cases, the FFP solution is in excellent agreement with existing asymptotic solutions; (ii) numerical overflow arises when the number of layers is large and/or the frequency is high, and a method to circumvent this difficulty is described; and (iii) the FFP is a most powerful tool in solving propagation problems in layered media bounded by complex impedances.