We have performed the ab initio calculations to study the role of correlation and relativistic effects in MAX phases. As of now, there are more than 50 MAX phases reported in the literature; however, we have chosen two MAX phases, namely Cr2AlC and Ta2AlC, as representatives of MAX phases for our study as they are very poorly described from calculation point of view. Our results show that correlation effects are very important to understand the electronic and mechanical properties of Cr2AlC, but not so important for Ta2AlC. We have also studied the relativistic effects on Ta2AlC and our calculations show that going from scalar to fully relativistic effects does not have any significant effect on the electronic and mechanical properties of Ta2AlC. We conclude that Ta2AlC is a weakly correlated system, whereas Cr2AlC is a strongly correlated system. Further experiments are needed to explain the discrepancy between theory and experiments.