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. Advantages of both algorithms (embedding technique and augmented formulation) can be utilized by hybridizing them. Usually the commercial vehicle dynamic Software programs adopt a relatively simple model, in which the suspension can be parametrized using characteristic curves. They are suitable for real-time simulation, but it is difficult to extend the model for other specific applications. For instance, the model cannot be coupled with virtual road simulator. The hybrid algorithm offers the possibility to extend given models easily and quickly to other use cases of multibody simulation. A structure of a vehicle with trailer model is described in this paper. The basic vehicle dynamic model presented in this paper includes the potential for real-time simulation and is also capable of extension for other applications such as simulation with virtual test rigs.