Much has already been seen in the world regarding the damage that may result from an accident in nuclear power plants. In the event of an accident that causes effective damage, either to the environment or to the population, both the Brazilian and foreign standards predict liability for remedying. The Brazilian Federal Constitution of 1988 determines the competence of the Union to operate nuclear services and installations, being State monopoly activities related to nuclear material and its derivatives. Besides that, FC/88 attributed liability stricto sensu for nuclear damage. The Vienna Convention on Civil Liability for nuclear damage, dated May 21, 1993, which was promulgated in Brazil by Decree No. 911/1993, provides that the operator is responsible for nuclear damages, in the case of Brazil, the operator is the State entity (Federal Autarchy) responsible for the operation. Thus, in cases of nuclear damage, the State should be held liable objectively. And here issues begin to arise such as: Is the State always responsible? Is there any possibility of exclusion of the State???s liability? This paper aims to analyze the constitutional text and the infra-constitutional rules in an attempt to answer these and other questions without, however, intending to exhaust the subject.