Key message: A novel multi-environment competition individual-tree mixed model resulted in better fit, and greater individual narrow- and broad-sense heritabilities than the model without competition, notably for traits showing competition. In multi-environment tests, the proposed model would allow tree breeders to select genotypes with the best performance in both additive direct and competition breeding values, increasing forest productivity. Context: Genetic merit of trees is known to be affected and interact with local competition effects as well as changes across environmental conditions. Recent studies showed that competition genetic effects can affect the genetic variance and bias the tree breeding values, and its covariance with direct breeding values has been variable across traits. Aims: The present paper extends a mixed-model methodology to the problem of accounting for competition in a multi-environment set of forest genetic trials and exploring its impact on genetic variances as well as the multi-environment genetic correlation. Methods: The proposed model is illustrated using data from two full-sib trials of Pinus elliottii var. elliottii × Pinus caribaea var. hondurensis F1. Dispersion parameters and (co)variance of total breeding values were estimated for diameter at breast height, total tree height, and stem straightness at age 10. Results: For traits showing competition effects (diameter at breast height and total tree height), the proposed multi-environment competition model gave better fit than the simpler model. Accounting for competition increased the direct additive variance, reduced the residual variances, and did not change significantly the across-site additive genetic correlation. However, for diameter at breast height, top 5% best genetic rankings showed differences. Conclusion: When traits are strongly affected by inter-tree competition, the use of the proposed model in multi-environment analyses can efficiently identify the phenomenon w