Bayesian estimates of variance-covariance matrix have been obtained. Two loss functions were used to estimate five Bayesian matrices of variance-covariance matrix S. The data included 1000 animals and five correlated traits, measured simultaneously on each animal. Determinant, traces, eigenvalues and eigenvectors were estimated for the Bayesian matrices. Weighting coefficients of five selection indices were calculated. The genetic gain of these indices was obtained. All estimates of phenotypic variance-covariance matrix used in selection indices computations have led to a close magnitude of the expected genetic gain. Different estimates of ∑ are all relative to a given loss function.