Investigating violations of the laws and customs of war is a relatively new area of activity for law enforcement agencies in Ukraine. Although some experience of such investigations has existed since 2014, the international armed conflict that began on February 24, 2022, identified almost all forms (methods) of violation of the laws and customs of war, which requires a comprehensive analysis and correct understanding of the rules of international humanitarian law that define the rules for participants in armed conflict. The purpose of the research is to define some circumstances to be proved in the course of the investigation of violations of the laws and customs of war and to disclose their content with due regard for the rules of international humanitarian law which determine the specifics of the object of proof in such criminal proceedings. The research employs philosophical (dialectical and hermeneutical), general scientific (systemic, historical, functional), and special scientific (comparative jurisprudence, technical-legal, and interpretation of legal provisions) methods of cognition. The work is based on the provisions of the treaty and customary law of armed conflict, the practice of its application at the national and international level, national law providing for liability for violation of the laws and customs of war, the procedural procedure for investigating criminal offences, and forensic recommendations for investigating particular types of crimes. Based on the results of the research, the author develops several circumstances to be proved in the course of investigation of the laws and customs of war as separate but related to other elements of the object of proof, namely: lawful combatants, combatant's immunity; territorial and time limits of international humanitarian law; legitimate purpose, military necessity. Their content, evidentiary value, and relationship are covered