Abstract: Methematic models for relationships of yield to water supply and planting density was established and analyzed based on data gathered from rainshelter and field experiments during 1986 - 1990. The relations of yield and water amount in any density could be considerably well expressed by a complex model ofIt was shown that a proportionate phase between increments of water (?w)and yield (?y) existed before the maximum yield was reached, and the upper crossing point(X1, Y1)between the parabola and the straight line was the locus suitable for water saving with high yield. The total water input for both water saving and high yield should be ranged from(X1, Y1)to the maximum of the parabola(Xm, Ym)with significant difference in total but no or less difference in that irrigated among years. When the same amount of water was given, the yield from water of 210mm given at stages of stem elongation, heading, and middle grain filling of wheat would be higher than any other watering patterns. The relationships of density and yield under any water conditions could be highly fitted by a deformed quadratic hyperbola Y = X/(A+BX +CX2).It was shown by this model that the density should be within 170 - 220 thousand plants per mu with no irrigation or water-saving irrigation patterns, and higher density would be needed when less irrigation or water stressed post-stem-elongation stages. Models above would be valuable in the establishment of integrated wheat husbandry modeling system for water saving.

Key words: Wheat, Water supply, Planting density, Yield model