The scattering loss of two-dimensional antiresonant reflecting optical waveguides (ARROW) and of ARROW-B, which has a similar structure to ARROW and less polarization dependence, are analyzed by the first-order perturbation theory. Calculated results are compared with those of conventional three layer waveguides. Optimum design for the reduction of scattering loss of these ARROW-type waveguides is discussed. It was found that the scattering loss of ARROW-type waveguides is no larger than that of a conventional waveguide having a relative refractive-index difference, Delta of 2.5%, despite each interface of ARROW-type waveguides having a large Delta , normally larger than 20%. The optimum design for the reduction of essential radiation loss of ARROW is also optimum for the reduction of scattering loss. >