Many genetic studies collect structured multivariate traits that have rich information about the traits encoded in trait covariates, in addition to the genotype and covariate information on individuals. Examples of such data include gene-environment studies where the same genotype/clone is measured in multiple enviroments, and longitudinal studies where a measurement is taken at multiple time points. We present a flexible multivariate linear mixed model (fMulti-LMM) suitable for genetic analysis of structured multivariate traits. Our model can incorporate low-and high-dimensional trait covariates to test the genetic association across structured multiple traits while capturing the correlations due to individual-to-individual similarity measured by genome-wide markers and trait-to-trait similarity measured by trait covariates.Linear mixed models (LMMs) are widely used for genetic mapping; an important feature is their ability to adjust for confounding due to genetic relatedness among individuals. They are used in genomewide association studies (GWAS) 1-7 to identify genetic loci contributing to traits of interest. Multivariate LMMs (MLMMs) enhance statistical power over univariate LMMs 8 because they can accumulate signals across traits 2, 9 for traits with a common genetic locus. Many