Abstract: The empirical functions of maize yield (Y) and water consumption (ET) under different regimes of water and fertilizer supplies were obtained from the field experimental data at Ansai Experimental Station of CAS. The coupled zones for optimal supplies of water and nutrients, for high yield and water use efficiency were identified through the established relationships. In the water and nutrient plain, the points for elasticity of water production (EWP) of 1 or 0 along two lines that leading to the maximum yield point and that of the yield gradient, formed two kinds of coupled zones of elliptical shape for optimal fertilizer and water supply, referred as the first and the second kind of ellipse, respectively. The minor axis of the second kind of ellipse is shorter than that of the first kind; however, the major axes are the same for two kinds of ellipse. And both Y_max and WUE_max were located at the ends of the major axes. Optimal supplies of water and fertilizer can be decided in the elliptical zone with additional considerations of other special requirements.