The authors of this paper focus on the simulation of the motor vehicle movement (taking into consideration motor vehicle dynamics, motor vehicle hydraulic brake system influence on motor vehicle movement, interaction between its wheels with road pavements, road guardrail characteristics, interaction between motor vehicle and road guardrail) on a certain road section and propose their specific solution of this problem. The presented results, illustrating the motor vehicle movement trajectories (motor vehicle braking and interaction between motor vehicle and road guardrail at various initial conditions and at various certain pavement surface of the road section under investigation) and work of a motor vehicle hydraulic brake system. Taking into consideration the presented general mathematical model and computer aided test results it is possible to investigate various road transport traffic situations as well as to investigate various transport traffic safety problems.