Purpose of research. The aim of this work is to develop an algorithm for sequential movements of a three-section crawling robot, which enables the device overcoming flights of stairs by crawling on each step or descending each step in the reverse sequence of stages. A special feature of the robot is the combination of three types of movement: snake-, worm - and caterpillar-like, which makes the device more maneuverable and expands its functionality. Methods. To develop a mathematical model of the movement of crawling robot sections at each stage of the algorithm and description of its contact interaction with the surface, the method of dynamics of multi-mass systems is used; methods of kinematic and structural analysis of the robot mechanism are used to form constraints that restrict the movement of the sections. Results. The article presents the results of simulation experiments of a robot crawling on a step of a flight of stairs and descending it, confirming the adequacy of the proposed movement algorithm. Positions of base points at the moments of the beginning and completion of the stages, section lengths and their turning angles in the vertical plane correspond to the values of these variables specified in the algorithm in the form of applied links and laid down conditions for the completion of stages. Conclusion. The article describes a detailed step-by-step algorithm for robot crawling on a step of a stairs flight and descending it; it is shown that crawling and descending are opposite operations from the point of view of sequence of stages implementing. The advantage of this algorithm is the versatility of its stages for moving the robot up and downstairs. In addition, the algorithm stages are designed in such a way that the robot does not roll over.