A method for computing nonlinear interactions between the spectral lines of progressive finite‐amplitude waves in homogeneous media is developed via Burgers' equation. By means of Fourier analysis, this equation is reduced to a coupled set of ordinary nonlinear differential equations, which are then solved recursively using Airy's algorithm. The solution thus obtained has the form of a vector which initially contains the spectral amplitudes of the source waveform and is subsequently enriched by nonlinearly generated spectral components as the signal propagates through the medium. The utility of the method consists in the ease with which it can be implemented on a digital computer and its applicability to a wide variety of source waveforms.