Stability of a car's trajectory of motion is the ability of a car to retain its required state of motion, under different conditions of motion. Depending on different states of motion, cars can lose direction of motion instability when there is a lateral force, due to vehicle speed, due to turning or braking the road with different grip coefficients on the sides of the wheel. In such complex moving conditions, cars need to keep a stable trajectory of movement under the driver's control. The paper examines the stability of the car's trajectory in linear motion conditions with the influence of lateral forces and the velocity of the vehicle, these two factors act to change the state of movement of the vehicle, which significantly affects the safety of the vehicle's movement. The authors looked at the effect of vehicle velocity and lateral forces on vehicle transverse dynamics: lateral forces caused by horizontal winds, inclination of the road surface, speed of movement of the vehicle acting on the entire body create centrifugal inertial forces; this force acts to cause the tires to deform. At this point the vehicle is shifted from its original trajectory. In the research content, the authors built a lateral Dynamics Model, in which the influencing factors are set as inputs to the model including vehicle velocity and transverse wind forces, output is the rotation angle of the body, transverse acceleration and horizontal displacement of the vehicle. The simulation results showed that the effect of vehicle speed was relatively large: lateral displacement increased by 228 % at a speed of 120 km/h. Therefore, when driving on the highway, there should always be driver control to ensure that the car does not deviate from the lane