Estimates of covariance functions and genetic parameters were obtained for growth of Angus cattle from birth to 820 days of age. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights were modelled through random regression on orthogonal polynomials of age at recording. A total of 11 combinations of quadratic, cubic, quartic and quintic polynomials to model direct and maternal genetic effects and permanent environmental effects were considered. Results showed good agreement for all models at ages with many records, but differed at the highest ages and at very early ages with few weights available. Cubic polynomials appeared to be most problematic. The order of polynomial fit for permanent environmental effects of the animal dominated estimates of phenotypic variances and mean squares for residual errors. A model fitting a quartic polynomial for these effects and quadratic polynomials for the other random effects, appeared to be the best compromise between detailedness of the model which could be supported by the data, plausibility of results, and fit, measured as mean square error.