In media for which the speed of sound is position dependent, propagating sound will be refracted and, in some cases, focused. In the focusing regions, usually referred to as caustics or convergence zones, significant amplification of the pressure levels above those predicted by spherical spreading has been observed for continuous waves as well as for explosive pulses. In addition, the waveforms of explosive pulses undergo drastic distortion. In the present paper, an asymptotic theory of the refraction and focusing of sound originating from a point source in a stratified medium is presented. It is applicable to realistic velocity profiles and encompasses both transient pulses and harmonic waves. A comparison with Barash's and Goertner's recent experiment involving explosive pulses indicates that the theory gives reliable estimates of the peak pressure levels at caustics, but reproduces only qualitatively the shape of the focused pulse. The discrepancy is attributed mainly to the neglect of finite‐amplitude effects in the theory's formulation. The inaccuracies inherent in the high‐frequency asymptotic methods employed in the theory are discussed in some detail.