For the development of effective vehicle related safety solutions to improve cyclist protection, kinematic predictions are essential. The objective of the paper was the elaboration of a simple mathematical model for predicting cyclist kinematics, with the advantage of yielding simple results for relatively complicated impact situations. Thus, the use of elaborated math software is not required and the calculation time is shortened. The paper presents a modelling framework to determine cyclist kinematic behaviour for the situations in which a M1 category vehicle frontally hits the rear part of a bicycle. After the primary impact between the vehicle front bumper and the bicycle, the cyclist hits the vehicle’s bonnet, the windscreen or both the vehicle’s bonnet and the windscreen in short succession. The head-windshield impact is often the most severe impact, causing serious and potentially lethal injuries. The cyclist is represented by a rigid segment and the equations of motion for the cyclist after the primary impact are obtained by applying Newton’s second law of motion. The impact time for the contact between the vehicle and the cyclist is yielded afterwards by formulating and intersecting the trajectories for two points positioned on the cyclist’s head/body and the vehicle’s windscreen/bonnet while assuming that the cyclist’s equations of motion after the primary impact remain the same. Postimpact kinematics for the secondary impact are yielded by applying linear and angular momentum conservation laws.