In this report, the design of a set of silicon-on-insulator (SOI) Mach-Zehnder interferometer (MZI) is proposed. The design intention of the MZI set is to extract waveguide group index \(n_g\). The theory of SOI waveguide, Y-branch and the MZI are presented. Then the modelling and simulation are performed to validate the design and provides insights to expected measurement results.