To date, radiation adaptation response has been reported as a low-dose related phenomenon and has been associated with radiation hormesis. Well-known cancers are caused by non-radiation active reactants, in addition to radiation. A model of suppression for radiation-specific cancers was previously reported, but the model did not target radiation-nonspecific cancers. In this paper, we describe kinetic models of radiation-induced suppressors for general radiation non-specific cancers, estimating the dose that induces the maximum hormesis effect while satisfying the condition that the risk is approximately proportional to dose above 100 mSv. It was found that the radiation hormesis effect is maximal at about 20 mSv when the rate constant for generation is the same as the rate constant for decomposition. When the two rate constants are different, the dose at which the radiation hormesis effect is maximized depends on both rate constants, but the dose increases as the two rate constants approach each other, reaching a maximum of about 20 mSv. This conclusion may lead to the discovery of unknown cancer suppressors at low doses and the development of cancer suppression methods in the future.