In this article we describe quantitative studies on the nonlinear piezoelectric effect in KNbO3 single crystals for a highly efficient surface acoustic wave elastic convolver. First, we demonstrate that a simple measurement of the nonlinear piezoelectric constant of e355 is very effective for quantitative estimation of the efficiency of an elastic convolver. Next, the third-order piezoelectric constants, e355, e333, and e344, in rotated Y-cut KNbO3 substrates are measured by varying the velocity under an applied electric field. Using the third-order piezoelectric constants measured, quantitative estimations of the convolution efficiency are discussed. © 2000 American Institute of Physics.