Based on the analysis of the developed mathematical model, this paper proposes optimal operating modes of the vibroimpact device to ensure the intensification of driving construction piles. It is an original design of a modern, highly efficient device for driving construction piles, equipped with a compact, powerful hydraulic impulse drive unit. To develop a mathematical model of the construction pile driving technology, the following methods were used: mechanoreological phenomenology, hydrodynamics, and generalised laws of mechanics. Mathematical models of the dynamics of technological processes of driving construction piles with a vibroimpact device are improved based on a hydraulic impulse drive unit in the form of a spatial non-stationary formulation of the problem and integral equations of dynamic characteristics of the moving elements of the drive unit. The study obtained the distribution of the pressure and velocity of the working fluid in the hydraulic unit of the vibroimpact device, as well as changes in the kinematic parameters of the elements of the technological equipment based on the mathematical model developed by the finite volume method, using numerical modelling and high-performance computer systems. Optimal modes of operation of a hydraulic impulse drive of a vibroimpact device are proposed to provide an intensification of the construction pile driving technology. It was found that when low-frequency vibration is applied, the driving of construction piles is intensified. Application of a hydraulic impulse drive that is based on two-stage vibration excitation allowed implementing the vibroimpact modes of the device. The average pile driving speed with a vibroimpact interaction is five times higher compared to conventional driving methods