Multivariate analyses of carcass traits for Angus cattle, consisting of six traits recorded on the carcass and eight auxiliary traits measured by ultrasound scanning of live animals, are reported. Analyses were carried out by restricted maximum likelihood, fitting a number of reduced rank and factor analytic models for the genetic covariance matrix. Estimates of eigenvalues and eigenvectors for different orders of fit are contrasted and implications for the estimates of genetic variances and correlations are examined. Results indicate that at most eight principal components (PCs) are required to model the genetic covariance structure among the 14 traits. Selection index calculations suggest that the first seven of these PCs are sufficient to obtain estimates of breeding values for the carcass traits without loss in the expected accuracy of evaluation. This implied that the number of effects fitted in genetic evaluation for carcass traits can be halved by estimating breeding values for the leading PCs directly.