A new fast field program (FFP) has been developed for numerical computation of sound pressure from a phased multiple‐source or multiple‐receiver system in a layered atmosphere. The new FFP is based on a far‐field approximation for which a criterion of validity is given. Using the stationary phase method, the twofold integral for sound pressure is reduced to a onefold integral representing the far‐field approximation of sound pressure. The onefold integral makes the new FFP very efficient.