We presents a dynamic modeling of 4-wheel 2-DOF. WMR. The classic dynamic model utilizes a greatly simplified wheel motion representation and using of a simplified dynamic model confronts with a problem for accurate position control of wheeled mobile robot. In this paper, we treats the dynamic model for describes relationship between the wheel actuator force/torque and WMR motion through the use of Newton's equilibrium laws. To calculate the WMR position in real time, we introduced the Dead-Reckoning algorithms and the simulation result show that the proposed dynamic model is useful. We can be easily extend the proposed WMR model to mobile robot of similar type and this type of methodology is useful to analyze, design and control any kinds of rolling robots.