Abstract: In this paper we develop a theory of nonlinear interaction for finite amplitude random sound waves. On the basis that the velocity amplitude of narrow band random vibration at the source of sound should obey Rayleigh’s statistical distribution, the authors extend successfully Fenian’s theory to the case of random sound waves. A series of interesting formula expressed in form of the spectrum resolution are derived （for example, the nonlinear progressive distortion of random sound waves, the suppression of weak random sound by intense regular sound, the parametric process of random sound waves, etc.）. This paper also points out that some important results of statistical phenomena of nonlinear acoustics obtained by O. V. Rudenko can be easily derived from the present theory.