In this paper, total internal reflection (TIR) mirror is carefully simulated for silicon nitride polygonal ring resonator sensor structure. Polygonal resonator has recently attracted much attention for applications in bio and chemical sensors because it does not have a bending loss, and it has an advantage of using MMI coupler. In polygonal resonator sensor design, high Q-factor and low TIR mirror loss are extremely significant factors. Therefore, critical angle and Goos-Hanchen shift should be considered in the design of TIR mirror. When cladding material is SiO2, the critical angle of SiNx waveguide is about 44.99 degrees and the Goos-Hanchen shift is about 400 nm at 1.55 μm wavelength. For the rib type waveguide, we designed it to have 3 μm width, 1 μm height, and 0.5 μm etching depth for decreasing TIR mirror loss. As simulation results of FDTD, reflectivitities of polygonal TIR mirrors are 79% for pentagon, 95% for hexagon and 98% for octagon, respectively. According to the simulations, Q-factors for hexagonal and octagonal resonators can be obtained as high as 1.55 x 104 and 1.72 x 104, respectively.