Drought stress is one of the most important abiotic stresses in agricultural production, which causes great damage to crops every year, especially soybean [Glycine max (L.) Merrill]. Soybean is a valuable oilseed crop that has the highest cultivation area among oilseeds in the world due to its high oil and protein content. To investigate the effect of drought stress on the stability of soybean yield [Glycine max (L.) Merrill], an experiment with 19 soybean genotypes was conducted in two environments without stress (weekly irrigation) and drought stress (biweekly irrigation) in a randomized complete block design with three replications in two consecutive years in Khorramabad. The results of the combined analysis of variance of grain yield in two experiments in two years showed that grain yield was significantly affected by the simple and interaction effects of year and genotype (P< 0.01). The percentage contribution of the variance of environment, genotype and genotype-environment interaction was 58.3, 20.7 and 16.04% respectively and for this reason the stability of the grain yield of the genotypes was evaluated through two graphical methods AMMI and GGE-biplot. The results of the comparison of the means showed that the highest grain yield was obtained in non-stress conditions in genotypes G2, G3, G4 and G13 and in drought stress conditions in genotypes G5, G9, G11 and G13. According to the biplot diagram of the two principal components IPC1 and IPC2 in the AMMI analysis method, the genotypes G2, G3, G4 and G16 were distributed in the center of the biplot in addition to high yield and had general stability in all environments. In this method, the genotypes with specific stability to non-stressed and stressed environments were also identified. In the GGE-Biplot method using polygonal diagram display, genotypes 9G, 11G, 13G had specific stability to the stress environment and genotypes 2G, 3G and 4G were compatible with the natural environment. Also, to simultaneously select the branch yield and stability of the genotypes, the display of the average environmental coordinate (AEC) line that passes through the coordinate axis was used, and genotypes 2G, 3G, 4G, and 13G, which were located near the ATC line, were in addition to high yield and had stability of performance in all environments. The results showed that the AMMI method was a suitable method for analyzing the stability of genotypes, given that it explained 99% of the variation in the genotype × environment interaction with the first and second principal components. In the AMMI1 model and grain yield, which explained 93% of the variation in the interaction, genotypes G2 and G3, G4, G8 and G16 had greater general stability in all environments, while genotypes G6 and G7 had higher grain yield and favorable specific adaptation to normal irrigation conditions. In the AMMI12 biplot model, genotypes G2, G3, G4 and G16, in addition to high yield, were scattered in the center of the biplot and were introduced as the most stable genotypes for both stress and non-stress conditions. Therefore, based on both methods, genotypes 2G, 3G, 4G, and 13G were identified as high-yielding and stable genotypes in both stress-free and stress-free conditions. Among them, genotype 13G in drought stress conditions and genotype 7G with special stability in normal irrigation are recommended for subtropical climates such as Khorramabad and can be used in future breeding programs.