In arid and semi-arid regions of the world, including Iran, soil salinity is one of the major abiotic stresses. One of the ways to achieve high performance in these areas is to use salt-tolerant varieties of wheat. Iran is known as one of the places where the D-genome originated and evolved. In order to evaluate the salt tolerance of Iranian genotypes based on the eight indices using analysis of variance, regression and an artificial neural network (ANN), 41 Iranian wheat varieties (Trticum aestivum L.) were planted in a randomised complete block design with three replications under two saline irrigation conditions, 0.631 and 11.8 dS m−1, in Kerman, Iran. Significant differences between the varieties were observed, and the significant two-way interaction of environment × varieties in combined analysis and non-significant correlation, 0.07, between the yield in two environments (yield in non-stress conditions, Yp, and yield in stress conditions, Ys) indicates the existence of genetic variation among varieties and the different responses of the varieties in both the environments. The indices of tolerance, geometric mean product (GMP), mean product (MP), harmonic mean (HM) and stress tolerance index (STI) were calculated based on grain yield evidence of positive significant correlation with Yp and Ys. Based on the ANN results, yield stability index (YSI), MP, GMP and STI were the best indices to predict salinity-tolerant varieties. The varieties selected based on these indices, such as Bolani, Sistan, Ofogh, Pishtaz, Karchia and Arg, produced high yield in both the environments. These results show that bread wheat originating from Iran has salt tolerance potential and can also be used in studies related to salinity tolerance mechanisms.