AbstractThe mathematical model of loaded block pulley trolley movement was developed based on Lagrange equation of the second genus. The differential equations of loaded trolley motion were given along with the relations for viscoelastic block pulley characteristics based on empirical observations. It was shown that the modeling block pulley dynamics could be substantially simplified by means of universal program complexes when considering the mass variation and the rope rigidity of block pulley negligible by changing its length.It was demonstrated that the loaded block pulley model could be geared as a subsystem for the computer dynamic model of lifting crane, when executing the axial force of upper block pulley, the movement of exit rope section and the rope tension force at this section by means of subsystem output parameters.The example of trolley motion start model was given for the simultaneous load lifting with at a constant speed with the use of three-mass model.