Acceptance of the Rome Statute poses a number of problems under domestic law; particularly ratification of this document raises issues of constitutional compatibility. The main problem that Ukraine encountered on the way towards ratification was compatibility of the Rome Statute with the Ukrainian Constitution. Ukraine found it necessary to amend the Constitution in order to overcome the incompatibility. The aim of the thesis is to examine critically the constitutional issues that have been raised during the ratification of the Rome Statute by Ukraine. It will be discussed the opinion of the Constitutional Court of Ukraine on the conformity of the Rome Statute with the Constitution of Ukraine, and its way in managing the constitutional problems in light of international practice and opinions of both international and national scholars. The thesis focuses on four main issues that questioned the Rome Statute’s constitutionality in Ukraine: the principle of complementarity, the irrelevance of official capacity, surrender of Ukrainian citizens to the Court and the enforcement of sentences of imprisonment in third states. It will be analyzed the nature of every specific problem, applying to provisions of the Statute and provisions of the Constitution of Ukraine.