We numerically investigated optical properties, including evanescent intensity ratio (EIR), effective refractive index (Neff), dispersion coefficient (D), and mode area (Aeff) of the silicon nitride trench waveguides fabricated by using conventional lithography. The waveguides are etched 3 μm deep with potassium hydroxide for triangle and trapezoidal waveguides, which is then followed by 3 μm thermal oxidation and 725 nm silicon nitride deposition. The waveguide with 725 nm thickness has an EIR peak of 0.025 when its bottom width Wbtm equals 0.65 μm. A thinner waveguide has higher evanescent intensity ratio, which can be used in sensing applications. The locations of EIR peaks correspond to the quasi-TM and TE mode boundary. Narrower waveguides mainly support quasi-TM modes, whereas wider waveguides can support only TE modes. As the waveguide width increases, higher orders of TE modes emerge. In addition, a boundary of TE single mode and multimode can also be linearly curve fitted, according to the starting points of TE higher modes, in order to provide the single mode condition of the waveguide. The waveguide dispersion can be engineered to be in the anomalous region while at the same time remain close to zero. The waveguide with 725 nm thickness and 0.2 μm bottom width has its anomalous dispersion region between the wavelength of 1356 nm and 1462 nm. The mode area decreases with increasing waveguide width. This is the first time we have studied the mode properties of trench waveguides systematically. The waveguide will find more applications in sensing and nonlinear fields with the help of this mode analysis.