Introduction. The development of the adaptive hydraulic drive with the volumetric tool-feeding speed control of the production machines using the example of the portable URB-2.5 drilling unit is considered. A hydraulic control circuit is developed for adapting the tool-feeding hydraulic drive to the discontinuous load on the main motion drive in the course of drilling. The circuit includes a multifunctional hydromechanical transmitter executing functions of the drilling process monitoring and the original hydraulic valve control that allows generating the control pressure of the tool-feed hydraulic drive. Materials and Methods . A generic mathematical model of an adaptive hydraulic drive with delivery control is developed. A computational experiment is carried out to identify processes in the original hydraulic motor control circuit and in the tool-feed drive as a whole. Research Results. New mathematical and computational models of the adaptive hydraulic drive with the volumetric method of the revolution control of the dual-mass dynamic system and the hydraulic control circuit with a hydromechanical multifunctional device are obtained. The processes running in the hydraulic control circuit are identified; the efficiency of the offered sheet-oriented solutions is proved. Quantitative and qualitative characteristics of the adaptive hydraulic drive, dependences of the tool feed and rotation velocities and their variation range are specified. Discussion and Conclusions. The obtained results can be used to create new drilling rigs with various characteristics. The application of the developed mathematical and computational models will allow reducing time and resource expenditures under designing an adaptive hydraulic drive of the drilling rig, and creating prototype models and commissioning activities.