The parametric mixing and harmonic generation of surface acoustic waves (SAW) has been treated by a new formalism in which the nonlinear wave equation and boundary conditions are rigorously satisfied at the sum and difference frequencies. The key features are analytical expressions for the spatial structure of modes which can be synchronously driven by volume forces and surface‐boundary conditions. After a propagation distance of a few acoustic wavelengths, the acoustic fields evolve into a linearly growing normal‐mode SAW. Equations are derived from which the nonlinear interaction cross sections can be evaluated and numerical results are given for a number of materials. Good agreement was obtained between experiment and theory fory‐xandx‐y&agr;‐quartz in the limit that the piezoelectricity is neglected.