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This paper describes a new hybrid algorithm for multibody dynamics in vehicle system dynamics which combines the advantages of both embedding technique algorithm and augmented formulation algorithm. An approach to vehicle dynamics modeling based on the hybrid algorithm is presented. Embedding technique algorithm has relatively small number of equations of motion. With help of this technique, an enhanced parametric vehicle dynamics model can be built, representing characteristic curves of suspension comprised in kinematic and compliance. Small number of equations enables the vehicle dynamics model to be simulated very efficiently. In comparison to embedding technique algorithm, the main benefit of augmented formulation algorithm is relatively simple for computer programming. With help of augmented formulation algorithm, the structure of the vehicle dynamic model can be easily extended.