The general linearized equations governing the propagation of sound in a dissipationless temperature‐ and wind‐stratified medium are derived. A formal integral expression is given for the field of a point source located in such a medium, when it is bounded by an absorbing plane under conditions which lead to the formation of a shadow zone. This integral yields the following approximate (high‐frequency) expression for the decay rate within the shadow|p|2 = (B/r) exp[−(n/c)f13(−c′−U′ cosφ)23r]. Herepis the acoustic pressure,ris radial distance from the source,Bis independent ofr, fis frequency in cps,cis sound speed,c′ andU′ are sound‐ and wind‐speed gradients at the ground surface, φ is the angle between the wind direction and the direction of sound propagation, andnis equal to 5.93 for a pressure release boundary and to 2.58 for a hard boundary.