This thesis presents a modern approach to the Method of Integral Relations implemented in the Python programming language. This work is based on South's reports on solving supersonic conical flows and Belotserkovskii's publications on solving supersonic flows over blunt bodies. The Python SciPy library is extensively used in this thesis. A root finder module is used to perform South's solution process, and the Runge-Kutta ODE solver with dense output is implemented to replicate Belotserkovskii's solution process. The implementation of Python makes the development efficient and serves as an open-source framework for future work to build on. This work focuses on the 1-strip approximation of MIR, and the results are compared against Belotserkovskii's 2 and 3-strip results, experimental data, and the modified Newtonian method. The current 1-strip method shows the agreements of predicting the normal shock standoff distance and the shock wave shape to results from both Belotserkovskii and experiments. Future work on higher-order approximations and additional high-temperature models is required to improve the prediction of MIR in the hypersonic flow region.