Abstract mixed models and multivariate analysis are powerful tools for selecting superior genotypes in plant breeding programs. The blup (best linear unbiased prediction) method has been used to predict genetic values without environmental effects. Furthermore, the fai-blup (ideotype-design index) procedure is especially valuable for plant breeding because of multiple-trait selection. This study aimed to determine the genetic potential of advanced wheat generations using reml/blup in combination with multivariate techniques for the selection of superior genotypes. The experiment consisted of eleven wheat (triticum aestivum l.) genotypes. The experimental design was randomized blocks, with three replications. Plant height, spike insertion height, number of tillers, number of spikelets, kernel width, hectoliter weight and kernel weight per plant were determined. The genetic parameters were estimated using the reml/blup methodology, and the fai-blup index was calculated using predicted genetic values. The genotypes ufsmfw 1-02, ufsmfw 1-05 and ufsmfw 1-04 show potential to increase the grain yield. The selection gains for number of tillers (14.63 percent) and kernel weight per plant (22.35 percent) indicate the potential to select superior genotypes.