The purpose of this study is to highlight certain aspects of the subject matter of criminal offense in crimes involving misappropriation, embezzlement of property or its conversion by malversation. The methodological framework of the study has been developed taking into account general scientific and special methods of scientific inquiry. A number of scientific methods have been applied, including dogmatic, hermeneutic, comparative, extrapolation and analogy. The author proves that the subject matter of misappropriation or embezzlement of somebody else’s property, set out in Parts. 1 and 2 of Article 191 of the Criminal Code of Ukraine, is property entrusted to a person or under his/her administration—that is, property over which the person has special authority. Entrusted is property that is transferred to a person for possession or use in accordance with a transaction or in connection with the performance of duties associated with the position held. Evidence that property is entrusted to a person is that this person actually possesses the property and this property is under his/her control. It has been established that property under a person’s administration should be understood as property that is not under the physical control of a person, but transferred to him/her by the owner or his/her authorized representative on the terms of granting this person a certain amount of rights to own, use and dispose of this property, which ensures the possibility of operational management of it to achieve a certain goal, determined by the owner or without such, that is, the person is granted a certain authority to manage and dispose of property. The criterion for distinguishing between entrusted property and property under a person’s administration is the nature of a legal relationship between the owner and the person: for entrusted property, this is a relationship with the actual possibility of ownership, that is, the person actually possesses property; for property under a person’s administration, this is a relationship with the presence of a certain amount of ownership rights over the property, in other words, the person may not physically possess it. It is emphasized that the definition of the subject of the criminal offense under Art. 191 of the CCU is inextricably linked to the establishment of crime subject status. It is noted that an official is a person who has authority under the position held and performs a range of functions consistent with that position, including: administrative and economic functions; organizational and executive functions; and functions as a representative of the government or local self-government.