Currently, the development of a self-driving car (SDC) is becoming increasingly popular, the full autonomy of which is achieved by automatic control of all its driving modes and maneuvers, including parking — the most common maneuver. The problem of parking automation is of particular relevance, as far as it allows not only to facilitate the process of safe parking, but also to increase the density of parked cars. The paper considers the control problem of automatic parking of SDC. The statement and formalization of the control problem of car parking taking into account the mechanical and spatial constraints ensuring the safety of the parking maneuver are given. Both classical and modern control methods of automatic car parking are considered. The classical control method of SDC parking is based on the utilization of widely used Dubins and Reeds-Shepp traffic models ensuring fast acting optimal car parking. At the same time, the algorithm of a fast-growing random tree RRT was used to construct a path between two points. Due to randomization, an important advantage of this algorithm is its independence from the geometric representation and dimension of the modeled environment of the car. The modern control methods of SDC parking are based on the use of intelligent methods and technologies. In present paper in contrast to the classical, "untrained" methods, the control method of parking based on machine learning is used. The problem of synthesis of control algorithm of SDC parking based on the machine learning method with reinforcement is posed and solved. A car parking algorithm implemented in Python using mathematical libraries Matplotlib and NumPy is synthesized. Computer verification of the synthesized algorithm was carried out and optimal values of machine learning parameters were determined.