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Background: Under rainfall condition, stability of grain yield in diverse environments has been one of the most important objectives of breeding programs. Stability analysis is the best method to test the relative performance of genotypes over environments. Thus the aims of this study are to select adapted and stable bread wheat genotypes based on some parametric and non-parametric index. Methods: The experiment was conducted during the four consecutive agricultural seasons (2016-17, 2017-18, 2018-19 and 2019-20) at the level of the experimental station of Setif (ITGC). Eight genotypes of bread wheat were tested following Stability soft program to calculate the parametric and non-parametric indices. Result: The association between Wricke's ecovalence (Wi²), the mean variance component (θi) and the Stability variance (ω²i) indices with respect to grain yield revealed that G1. G2. Hidhab. Arz. Wifak and Ain Abid are suitable genotypes for growing under variable environmental conditions. In addition, selection based on the non-parametric index and the combination selection based on highest grain yield with the parametric and non parametric indices proved that the genotypes G1. G2 and Wifak are more stable and adapted genotypes under semi-arid conditions. Further, based on the static and dynamic concepts, the parametric indices, bi and CVi are related to the dynamic concept, while the other indices are associated with static stability concept. Overall, the results of this study confirmed that the parametric and Non-parametric methods are suitable tools to identify the most stable bread wheat genotypes under various environmental conditions. [ABSTRACT FROM AUTHOR]