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To provide information that can contribute to the genetic evaluation and selection in Tabapuã cattle, genetic parameters were estimated for growth traits using a multi-trait animal model. (Co)variance components were estimated by a Bayesian approach using the Gibbs Sampler. Moderate and similar responses to selection are expected when selecting for weights at the four ages evaluated, since the direct heritability estimates were similar and of average magnitude (0.18 to 0.19). The direct and maternal additive genetic correlations between all pairs of weights were higher than 0.70, indicating a high degree of association between the four traits. This suggests that using any of them as selection criteria will result in correlated response in the others and that multi-trait analysis are recommended for the genetic evaluation of growth traits in beef cattle for exploiting this association.