The paper deals with the mathematical model development of the kinematical behavior of the flexible transmission branch exemplified. A typical example of transmission with discrete-flexible connection can be considered as the movement of the drive elements of the chain. The use of chain gears as a drive for a wide range of technological machines with high requirements in order to ensure a certain law of motion of the executive bodies is the task of studying changes in its kinetic characteristics during operation. It is established that random deviations of the chain step from the nominal are the result of manufacturing inaccuracy elements of transmission and wear during operation. The mathematical model of motion gives an idea of the real interpretation of the kinematics of the chain transmission taking into account the uneven dimensions of individual links. The model makes it possible to present the components of deviations of the transmission movement from the given in two groups: deviations created by the accumulated error of the chain section, and movement. Calculations based on the developed mathematical model show that when the hinges of the sleeve-roller chain are worn by 2.5%, the value of the coefficient of non-uniformity of the transmission increases threefold.