The land transport sector has passed through multiple phases of evolution in design, development, manufacturing of vehicles. In particular, the construction site continues to progress towards the full automation with the automated driving functions. Noting that the autonomous vehicles (also called self-driving) were one of its big trends and have become a hot topic in rail and road transport world. By developing this new technology of assistance systems that control the hydraulic actuators of a car (steering wheel, accelerator, and brake driving), human is free from the driving tasks and the autonomous machine can move and execute different tasks autonomously in a construction zone, so the number of traffic accidents, depends on driver reaction, is reduced. The modeling and simulation phases had become necessary to simulate and assess the vehicle dynamics behavior, so the automated functionality will be easy to perform, the safety will be improved in high accuracy and the cost of development will be decreased. This work presents the design and implementation of a mathematical hydraulic model of Metalliance's vehicles which are actuated hydraulically and powered by a thermal engine (Metalliance, company that designs, industrializes, manufactures, and markets mobile machinery used or the construction and renovation of tunnels). The current model was implemented on Matlab/Simulink based on mathematical equations considering the machine's physical properties, hydraulic powertrain needs and the values of different vehicle parameters. Several tests with experimental tunnel recordings were carried out to verify the right action of the system and its fidelity to the real world.