Aim. We aim to test the hypothesis that radiation pressure from young star clusters acting on dust is the dominant feedback agent disrupting the largest star-forming molecular clouds and thus regulating the star-formation process.Methods. We performed multi-frequency, 3D, radiative transfer calculations including both scattering and absorption and re-emission to longer wavelengths for model clouds with masses of 10⁴–10⁷ M_⊙, containing embedded clusters with star formation efficiencies of 0.009–91%, and varying maximum grain sizes up to 200 μm. We calculated the ratio between radiative and gravitational forces to determine whether radiation pressure can disrupt clouds.Results. We find that radiation pressure acting on dust almost never disrupts star-forming clouds. Ultraviolet and optical photons from young stars to which the cloud is optically thick do not scatter much. Instead, they quickly get absorbed and re-emitted by the dust at thermal wavelengths. As the cloud is typically optically thin to far-infrared radiation, it promptly escapes, depositing little momentum in the cloud. The resulting spectrum is more narrowly peaked than the corresponding Planck function, and exhibits an extended tail at longer wavelengths. As the opacity drops significantly across the sub-mm and mm wavelength regime, the resulting radiative force is even smaller than for the corresponding single-temperature blackbody. We find that the force from radiation pressure falls below the strength of gravitational attraction by an order of magnitude or more for either Milky Way or moderate starbust conditions. Only for unrealistically large maximum grain sizes, and star formation efficiencies far exceeding 50% do we find that the strength of radiation pressure can exceed gravity.Conclusions. We conclude that radiation pressure acting on dust does not disrupt star-forming molecular clouds in any Local Group galaxies. Radiation pressure thus appears unlikely to regulate the star-formation process on either local or global scales.