The paper presents a method of modeling dynamics of multibody systems with open and closed kinematic chains. The joint coordinates and homogeneous transformations are applied in order to formulate the equations of motion of a rigid body. In this method, constraint equations are introduced only in the case when closed subchains are considered or when the joint reactions have to be calculated. This allows the number of generalized coordinates in the system to be reduced in comparison to the case when absolute coordinates are applied. It is shown how the method can be applied to modeling of vehicle dynamics. The calculation results are compared with those obtained when the ADAMS/Car package is used. Experimental verification has been performed and is reported in the paper, as well. In both cases, a good correspondence of results has been achieved. Final remarks concerning advantages and disadvantages of the method are formulated at the end of the paper.