When developing robotic assembly technology, it is necessary to use intelligent algorithms that control the assembly process online. One of the tasks that has been little studied so far is the assembly of cylindrical non-rigid parts. Mathematical models of the coupling stages during robotic assembly have been developed, which are necessary for the identification of the signals of the force-torque sensor. The obtained analytical solutions make it possible to determine the conditions for the occurrence of jamming of the non-rigid shaft during two-point contact during the coupling of the shaft with a rigid sleeve. The obtained values of deflections and angles of rotation allow us to correct the movement of the output link of the robot during the assembly operation. A mathematical model is presented for solving the problem of determining the current contact state (CS) during assembly using the support vector machine (SVM) method when obtaining information about the position coordinates by the control system of an industrial robot and forces from a force-torque sensor. The algorithm was tested on an IRB-140 industrial robot with an IRC5 controller equipped with an FTN-AXIA80 SI500-20 Ethernet force-torque sensor from Schunk.