The main types of structures of walking robots are considered and the choice of the design of the implemented layout of a six-legged insectomorphic robot is justified. Based on the results of the analysis of known approaches to the design of walking systems and the selected type of robot, solutions of forward and reverse kinematics problems for its joints are described. Kinematic and dynamic models of a six-legged walking robot are calculated and implemented programmatically. A computer simulation model of a six-legged walking robot is constructed that combines a 3d representation of the robot and the dynamics of its movement. The procedure for adjusting the control algorithms for a multi-link structure is suggested to adapt for the uncertainties in the robot construction and the surrounding environment. Verification of the proposed mathematical models was carried out on virtual and hardware samples of walking robots