This paper presents an extended kinematics and dynamics of the articulated tracked vehicles (ATV) used in many applications. The velocity of the front and the rear vehicle are firstly analysed and the kinematics of ATV is built, according to which the steer radius and the track velocity can be obtained. Then we analyse the force and moment acting on the ATV running on the firm ground and the soft ground, respectively. And a unified dynamics is established in a matrix form. To show the motion performance of the ATV, simulations are performed and the results are further presented.