The sound generated by the nonlinear interaction of two sound beams of high intensity, arranged to cross each other perpendicularly, is computed to the first order of interaction. Several of the assumptions and specializations in previous treatments of this problem, whose effects on the result it is hard to estimate, are avoided. The interaction is supposed to take place in the Fraunhofer zone of both beams.Some results obtained are of general validity. For instance, the Doppler angles computed and measured by Ingard and Pridmore‐Brown are found, without any strict specializations of the primary beams and the interaction region.Estimates of the amplitudes of the generated pressure, governing rather wide ranges of frequencies of the primary beams, seem to agree with the previous apparently strongly differing results. This correspondence is brought forward by an amplitude factor, depending on the frequencies of the primary beams.In the high‐frequency limit, the destructive interference among the quadrupoles which give rise to the generated sound dominates the results and gives an over‐all zero value of the generated pressure, in accordance with Westervelt's treatment.