Classical multivariate mixed models that acknowledge the correlation of patients through the incorporation of normal error terms are widely used in cohort studies. Violation of the normality assumption can make the statistical inference vague. In this paper, we propose a Bayesian parametric approach by relaxing this assumption and substituting some flexible distributions in fitting multivariate mixed models. This strategy allows for the skewness and the heavy tails of error-term distributions and thus makes inferences robust to the violation. This approach uses flexible skew-elliptical distributions, including skewed, fat, or thin-tailed distributions, and imposes the normal model as a special case. We use real data obtained from a prospective cohort study on the low back pain to illustrate the usefulness of our proposed approach.