The aim of the present work is to establish the parameters of the relationship additional yield – irrigation depth for sunflower grown in the region of Plovdiv, using different equations of the following kind: /1/ y=ax2+bx; /2/ Y=1–(1–x)n. The source data used for the study are from a field experiment, carried out in the region of Plovdiv (Bulgaria) on alluvial-meadow soil, with the sunflower hybrid PR-64-E-83. Variants of the field experiment are: 1 – without irrigation; 2, 3 and 4 – with irrigation, applying 50%, 100% and 150% of the irrigation rate, determined by the optimal variant (pre-irrigation soil moisture 75% of FC for the 0 – 80 cm layer). If we accept that the relative irrigation depth is 1.000 in variant 4, then the relative irrigation depth in the other variants is as follows: var.1 – 0.000, var.2 – 0.333 and var.3 – 0.667. The results show that equation /1/ is most suitable from a mathematical point of view. The representative type of equation /1/ is: Y=2.743x–1.745×2 by R2=1. The variations of the calculated yields using this equation to experimental yields are from -10.2 to +6.8% (R=0.998). Equation /2/ is also very accurate from a mathematical point of view and at the same time corresponding well with the biology of the crop. The variations of the calculated yields using this equation toexperimental yields are from -8.4 to +15.8% (R=0.993). The following parameters are established: n=3.37(from 2.34 to 4.67) and R=0.997 (from 0.986 to 1.000). All established parameters of the relationship yield– irrigation depth in this paper are valid when moistening the 0–100 cm layer and 75% FC pre-irrigation soil moisture is maintained for the soil layer of 0 to 80 cm.