Wheat production is a crucial component of global agriculture. However, it faces numerous challenges, particularly in the context of global warming and climate change. In order to address the challenges facing wheat production, such as declining irrigated lands and average rainfall, it is important to develop cultivars that can thrive in dry and stable conditions. The stability of a plant is defined as the ability to survive in a specific environment, where it can be evaluated in different ways such as univariate and multivariate parametric methods and non-parametric methods. To this end, it is crucial to study factors such as genotype × environment interactions and select stable cultivars using a mixed model that includes both fixed and random variables. The interaction impact of genotype × environment can be divided into two parts: crossover (imperfect genetic correlations of traits) and non-crossover (heterogeneity of genetic variance in the environment). In random models, it is not possible to estimate the treatment effect directly. Instead, the treatment effect needs to be predicted, which introduces the potential for errors. These errors occur because the prediction of the treatment effect may not be perfectly accurate. Such error can be minimized using the BLUP method (best linear unbiased prediction). Therefore, in this study and to evaluate the error, we combined the AMMI and BLUP methods using a mixed linear model based on the BLUP method. The aim of this study was to select the superior lines in terms of performance and stability among 16 advanced bread wheat lines using a combination of the AMMI and BLUP methods along with the WAASB and WAASBY indices, as well as interpreting the relevant graphs to better understand genotype × environment interactions.