The article discusses the functional-structural scheme and the mathematical model of the working hydrodynamic processes in the throttle-adjustable hydraulic drive of the technological cranes-manipulators. The model allows to perform computer simulations of the kinematics and dynamics of the elements of the metal structure of the manipulator and hydrodynamic working processes in the hydraulic drive as jointly occurring and interacting processes. A description of a computer program that implements the developed mathematical model is given. The program allows to calculate the change in time of movement, speed and acceleration of the moving link of the handling system, pressure and volumetric flow rate of the working fluid in the characteristic points of the hydraulic system and a number of other parameters. The operation of the hydraulic drive of the real manipulation system was simulated and the obtained results were analyzed. The adequacy of simulation results and real physical phenomena observed during the operation of mobile machines is shown.