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This review aimed to estimate covariance components for Tabapuã the growth characteristics in Brazil, using random regression models. The random regression models (MRA) make it possible to estimate coefficients of the covariance functions by the method of restricted maximum likelihood. These are suitable for longitudinal data analysis models, because of the deficiencies of conventional methods of quantitative genetic analysis, which are considered phenotypic values inherently continuous processes, as discrete processes. The covariance functions show the statistical correlation between two features of a trajectory at different points of same, ie that present in the arrangement have the same direction and magnitude. With the current concern of cutting bovinocultores regarding the growth of animals, the use of methods or techniques that provide increasingly accurate assessments of genetic parameters to be used in studying the development of animals for meat production is relevant