Various studies on motorcycle rider whole body vibration (WBV) exposure indicate that the vibration magnitude in the vertical direction is the most severe as compared to magnitudes in lateral and transverse directions. For the sake of understanding and doing evaluation of the vibration environment of the motorcycle rider and various motorcycle component bodies, a mathematical model was developed. The main intention was to investigate the physics of motorcycle suspensions, study vibration magnitudes in vertical direction in terms of displacement and acceleration on a cyclist depending on motorcycle and road parameters, also attempt to determine the location of the rider’s seat with least vibration magnitudes. In this case, analytical methods for studying response to harmonic base excitation of the rider and other component bodies of a motorcycle were applied with the aim to analyze their vibrational behaviour. The two wheeled motorcycle with a rider model was introduced. The equations of motion for the model were formulated. The matrix form of the equations was written solved and simulations were done. The vibration behaviour in vertical direction of various component bodies of the motorcycle model was observed.