The present article examines the concepts of natural person, passengers, travelers, who travel across the state border through the state border and customs border crossing checkpoints, for various purposes. The author indicates in the article the types of transport that may be used by individuals when moving across the state border and the customs border of the state, through the state border and customs border crossing checkpoints, also indicating animal traction transport and live animals that can be used as objects of travel and means of movement across the state border and the customs border of the Republic of Moldova. In the article, the author also carries out a analysis of the legislation of the Republic of Moldova on the application and use by individuals of animal traction transport, including live animals as a means of transport and travel across the customs border of the state, appealing in this regard to the practice of law enforcement bodies in some states of the European Union.