There are quite few publications where the representation of transient states of tyres is taken into account in the examination of the motion of a vehicle as a whole by computer simulation. Most of the researchers who build models of motor vehicle dynamics leave this issue out of account, believing that it is related to the phenomena of little importance in both qualitative and quantitative terms, especially when self-excited vibration of wheels with pneumatic tyres is ignored. The objective of this publication is to present simulations of motor vehicle motion in the situation encountered during the training of drivers at Driver Improvement Centres. The author proves that the taking into account of the representation of transient states of the lateral force and aligning moment on vehicle tyres will strongly affect the calculation results. This is because of the excitation form, the time constants of which are comparable with the relaxation time of the tyres of the vehicle under test. The analysis results have been presented in both quantitative and qualitative form, i.e. in a table and as time histories of selected quantities, respectively. The data shown indicate considerable differences in the calculated effects of disturbance to rectilinear motion of a passenger car, when determined with ignoring the transient states of tyres, in comparison with the corresponding calculation results obtained with the transient states of tyres having been taken into account. The biggest differences in the absolute values recorded during the first second from the beginning of the disturbance to the motion of rear vehicle wheels were observed in yaw (heading) angle, lateral displacement of the centre of vehicle mass, and moment of forces on the steering wheel. The differences were so big (from 19 % to 26 %) that they changed the qualitative and quantitative assessment of vehicle behaviour. Thus, they highlighted the great impact that the representation of transient states of the lateral forces and aligning moments on vehicle tyres exerts on the results of the test being simulated.