Nowadays, quite a lot of methodology has been developed for the analysis of longitudinal studies, stemming from clinicaltrials, epidemiology, and other studies in humans. For example, hierarchical models are becoming evermore frequently. Such hierarchical models are standard in the analysis of longitudinal data, too to account the correlation steaming from the repeated measures nature. This study will be dedicated to model models for longitudinal continuous, firmly rooted inhierarchical models such as the linear mixed model. The Bayesian implementation of the models will also be explored using the freely available software WinBugs. The two approaches will then be applied on dataset from the Jimma Infants longitudinal growth study. The result demonstrated that the ML estimate sof the random effects standard deviations are smaller than the corresponding REML estimates which is different result from the Bayesian. The estimated within group residual standard deviations are identical. In general, the fixed-effects estimates obtain using ML, REML and Bayesian techniques are almost similar. The mean evolution of the upper arm circumference of infant for boys and girls is not different.