This study is an investigation of analytical and numerical predictions of the relativistic perihelion shift of the planets in the Solar System. These shifts are a consequence of the general theory of relativity and the theoretical expression for the perihelion shift can be derived using different approximations. Two of these approximations are presented in this report. Due to these approximations, it is of interest to investigate when the analytical expression provides accurate values of perihelion shifts. This is performed by calculating the perihelion shifts for the planets in the Solar System numerically and comparing the results. To summarize the results, the numerical method slightly outperforms the analyt- ical method for almost all planets in the Solar System but the results are overall similar. Furthermore, a parameter study is conducted to investigate how the numerical and an- alytical perihelion shift predictions are dependent on these parameters. The parameter study shows that the methods diverge for some cases and based on this predictions are made for when numerical methods could be of use when predicting perihelion shifts.