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We present an approximate semianalytical technique for the calculation of the loss coefficient of leaky modes in 3-D hollow dielectric waveguides having an arbitrary cross section. The hollow waveguides are assumed to have an axis of symmetry and to have a cladding with a higher refractive index than the core. An expression for the modal loss coefficient is derived using a ray-optics approach with paraxial approximation. For the special cases of specific cross sections with known solutions, our technique gives results that are identical to the available analytical solutions. The technique is then applied on practical waveguide geometries, allowing the calculation of polarization- and wavelength-dependent losses. Full numerical alternatives to the technique involve time-consuming simulations and, sometimes, difficulty in incorporating a suitable boundary condition to obtain leaky-mode solutions.