A statistical approach for the analysis of multi-environment trials (METs) is presented, in which selection of best performing lines, best parents, and best combination of parents can be determined. The genetic effect of a line is partitioned into additive, dominance and residual non-additive effects. The dominance effects are estimated through the incorporation of the dominance relationship matrix, which is presented under varying levels of inbreeding. A computationally efficient way of fitting dominance effects is presented which partitions dominance effects into between family dominance and within family dominance line effects. The overall approach is applicable to inbred lines, hybrid lines and other general population structures where pedigree information is available.