A simulation approach was used to determine the effects of multitrait selection on the correlations of sire direct and maternal predicted breeding values across environments. True and predicted direct and maternal breeding values (BV) of sires were simulated for sires evaluated independently in two different environments. Prediction error variances and covariances among direct and maternal BV within environments were required for the simulation. To obtain the necessary input parameters, a variety of MME coefficient matrices were created and inverted to inspect relationship among accuracies and correlations of prediction errors in sire evaluation models. An empirical prediction equation to predict the necessary prediction error covariances was obtained. Divergent, directional and random multitrait selection was then practiced using direct and maternal predicted BV as selection criteria. Samples of 40 sires were randomly obtained from each selected population. Observed correlations between direct and maternal predicted BV across environments were compared to expectations derived from univariate distribution theory. Selection definitely affected the expectations. However, the adjustment developed from univariate theory appeared to accommodate the effect of selection in these expectations. / Ph. D.