The single shot damage thresholds of multilayer optics for high-intensity short-wavelength radiation sources are theoretically investigated, using a model developed on the basis of experimental data obtained at the FLASH and LCLS free electron lasers. We compare the radiation hardness of commonly used multilayer optics and propose new material combinations selected for a high damage threshold. Our study demonstrates that the damage thresholds of multilayer optics can vary over a large range of incidence fluences and can be as high as several hundreds of mJ/cm(2). This strongly suggests that multilayer mirrors are serious candidates for damage resistant optics. Especially, multilayer optics based on Li(2)O spacers are very promising for use in current and future short-wavelength radiation sources.