At present, satellite-based limb-viewing measurements in near-UV, visible, and near-IR wavelength range are based on the attenuation of direct solar light (the Stratospheric Aerosol and Gas Experiment instruments). This paper studies a new technique: the measurement of backscattered solar radiance spectrum in limb-viewing geometry. A multiple-scattering backward Monte Carlo algorithm Siro has been constructed for realistic radiative transfer modeling of these measurements. By Monte Carlo simulation the difficult spherical geometry of limb-viewing can be accurately modeled, as can constituent densities and boundary conditions that vary in three dimensions. Previous multiple-scattering models applicable to limb-viewing all assume a spherical shell atmosphere. The backward technique is very efficient for simulating a receiver that has a narrow field of view. In this paper the role of multiple scattering is studied by the Siro model in an atmosphere including scattering by molecules and aerosols and absorption by O3. Simulations show that the multiple to total scattering ratio increases from almost zero at 300 nm to ~5--60% at visible and near-IR wavelengths (depending on solar geometry and albedo of Earth's surface). A single-scattering model is not sufficient for the analysis of limb radiance measurements. When the solar zenith angle is small, limb radiance is very sensitive to the surface albedo. A bright spot of diameter 50 km on an otherwise dark surface already causes a noticeable increase of intensity. ¿ 1999 American Geophysical Union