The study was designed to examine th e application of linear mixed model to incompleternblock designs. In addition to thi s, it is planned to compare VARCOMP, ML and REMLrnestimation methods for variance components of linear mixed models. Sixty three promisingrnbar ley lines and one standard check cultivar which were obtained from EIAR have beenrnevaluated for grain yield performance and adaptation across eight environmentsrn(combination offour lo cations by two ferti lizers).rnThe mean grain yields for individual line ranged from 17.06 to 33.21 quintals per hectarernand the mean grain yields for in dividual environment ranged from 16.80 to 44.214 quintalsrnper hectare. The highest mean grain yield was observed at BEKOjl, while the lowest meanrngrain yield was registe red at SHENO with both fertilizers doses (100 and 150 kg). When werncompare each variety with specific environment, lin e 8 and 55, Variety 20 and 14, Varietyrn49 and 54 and Variety 48 and the Local check to be ada pted and have best mean effects tornBEKOJI, SHENO, HOLETTA and NORTH GONDAR respectively.rnKEML estimates for vari a nce components are in distinguishable from classical techniques inrncase of balanced data. This im pl ies optimal minimum variance properties and REMLrnestimates do not rely on normality assumption. But, for unbalanced data, the REMLrnestimation for variance components is different from classical estimates. We have seenrnfrom the diffe rences that estimation of variance components benefits from REML bu trnVARCOMP does not. Therefore, the REML approach is appropriate to estimate va riancerncomponents in SLD and SLD with missing plots.rnVarieties/lines listed above were recommended to release in Ethiopia that have similarrnecologic zones of respective location s and REML techniques was recommended to be usedrnfor va riance components esti mates of linear mixed model for SLD and SLD with missingrnplots. It was found that diagnostics for Linear Mixed Model applied to estim ate variancerncomponents are perh aps an area that needs exploration in the future.