The complex problem of the spatial motion of the "trolley-beam" mechanical system is investigated. Three stages are considered: 1) movement of the beam on a bifilar suspension to the movable trolley; 2) movement of the beam after the breakage of one branch of the suspension; 3) movement of the beam after the breakage of the second branch of the suspension. The study was carried out by creating mathematical models for each stage of the system movement and then conducting a numerical experiment using computer algebra. The tension of the ropes is calculated at the first and second stages of the system movement. Their extreme values are determined. The obtained results will be used in the further study of the system to reduce the tension of the rope and oscillation amplitude and to prevent accidents.