This article is the second part of the publication with the same title, which appeared in the issue no. 4/2023 of the “Insurance Law”. The first part discussed selected differences in the regulation of civil liability of the operator of a nuclear installation for nuclear personal injury between the Nuclear Law Act and the Vienna Convention. Those included the definition of nuclear personal injury, the limitation period for claims for such injury and the rules for seeking compensation thereof. The Vienna Convention sets minimum protection standards in the event of nuclear damage, which has served as a benchmark for developing the principle of civil liability insurance of the operator of a nuclear installation for nuclear damage.The second part of the article deals with practical issues and provides a summary of the most crucial information concerning nuclear insurance market. It clarifies the notion of a nuclear insurer and their available insurance options. It also discusses the major elements of the civil liability protection for nuclear damage which differ from the rules of the insured’s civil liability specified by law. Finally, it addresses obstacles which may hinder the offering of this type of insurance as compulsory insurance under national legislation. This Article concerns solely the rules for civil liability for nuclear personal injury suffered as a result of operating the nuclear power plant. Insurance aspects related to the transport of nuclear material from nuclear facilities, the operation of research reactors and radioactive waste repositories have been omitted.