Technical Abstract: Six empirical functions were compared for describing the product yields of agricultural crops grown while subject to increasing levels of root-zone salinity. The four nonlinear functions fit the test data from a spring-wheat (cv: Biggar) experiment conducted in Canada's Salt Tolerance Testing Facility closer than the two linear functions. Although each of the four nonlinear declining functions could reasonably describe the data, the modified compound-discount equation recorded the lowest root mean square error and the highest R2-value. This is a sigmoidal function [Yr=1/(1+(C/C50)exp(s C50)] which relates relative yield (Yr) to a measure of root-zone salinity (C) such as the solute concentration with an electrical conductivity of an equivalent saturated soil paste extract (ECe). This function features two parameters, the salinity level producing 50 percent of the non-saline crop yield (C50) and the absolute value of the general decline in relative yield with salinity at and near C50, the steepness constant (s). These parameters combine to form a single-value, salinity-tolerance index (STI) consisting of the 50 percent reduction in crop yield (C50) plus the tendency to maintain some product yield as the crop is subjected to increasing salinity levels approaching C50, i.e., STI=C50+s(C50). The STI for the Biggar wheat registered 6.44. Approximations for C50 and s can be derived from the threshold salinity (Ct) and declining slope (b) parameters of the threshold-slope linear response function [Yr=1-b(C-Ct)]. Procedures for converting Ct to C50 and b to s offer linkages between these linear and nonlinear response function parameters, and are further explored in this paper's companion (Root-Zone Salinity: II. Indices for Tolerance in Agricultural Crops, by Steppuhn, van Genuchten, and Grieve, 2003). The resulting STI-values equal 6.56, 9.43, and 5.67 for sample field (corn), forage (alfalfa), and vegetable (radish) crops, respectfully.