A simplified modeling approach of free vibration for occupied car seats was demonstrated to be feasible. The model consisting of interconnected masses springs and dampers was initially broken down into subsystems and experiments conducted to determine approximate values for model parameters. Which were each stiffness and damping value. Nonlinear equations of motion were derived and model parameters obtained in experiments were applied to these equations. A mathematical model of free vibration for car seat and mannequin system was built with 7 degrees of freedom. in order to calculate natural frequencies and the corresponding mode shapes. linear equations of motion were obtained through linearization. In order to explore the effects of each model parameter free vibration analysis were preformed.