This article presents a new method for studying wave propagation in an unbounded medium where the square of the refractive index is of a general three‐dimensional quadratic form. By this method, the Green’s function can be expressed exactly by a onefold integral, for which the integrand is derived from a path integral. The numerical results for one‐dimensional Green’s functions in linearly stratified media are first checked with those obtained from the well‐known Airy function expressions. The method is then applied to obtain the three‐dimensional Green’s functions for linear stratified media and for parabolic profiles with range‐dependent (horizontal) variations. Some interesting phenomena caused by the horizontal variations (i.e., range dependence) of the medium will be shown and interpreted by simple ray pictures whenever appropriate. For the special case of a parabolic profile with symmetric turning points, a wave duct is formed and the Green’s function can be expanded as a series of wave modes. It will be shown that an evanescent mode in a purely stratified medium may switch to a propagating mode due to the range dependence of the medium property. Application of the results to acoustic wave propagation in the atmosphere and in the ocean will be discussed.