This paper describes the analysis of integrated optical waveguides using Finite-Difference Time-Domain (FDTD) method, and proposes the design methodology for low loss waveguide components: corner bends and branches. In order to integrate optical waveguides with Si VLSI technologies on a chip, the compact bends or branches are necessary. Since the optical power radiation from a bend or a branch point depends on the waveguide shapes, an accurate analysis of guided wave behavior is required. For the purpose we adopted the FDTD method which can analyze optical waveguides with a large variation of refractive index and arbitrary shape. Proposed design concept is to have all waveguides transmit only the fundamental mode and to design whole waveguides based on the fundamental mode transfer characteristics. For this design concept, waveguide components are required to have not only low radiation loss but also a little mode shift from the fundamental mode. The bend using the double-reflection mirrors and the branch using a slit are proposed for suppressing the mode shift and improving radiation loss. By the FDTD analysis, the following results have been obtained. The radiation loss and mode shift of double reflection bend are 1% and 4%, and those of the slit branch are 2% and 5%, respectively, in 2 µm width waveguide.