The objectives of this study were to develop models of the hand-arm system in the three orthogonal directions (x_h, y_h, and z_h) and to enhance the understanding of the hand vibration dynamics. A four-degrees-of-freedom (DOF) model and 5-DOF model were used in the simulation for each direction. The driving-point mechanical impedances distributed at the fingers and palm of the hand reported in a previous study were used to determine the parameters of the models. The 5-DOF models were generally superior to the 4-DOF models for the simulation. Hence, as examples of applications, the 5-DOF models were used to predict the transmissibility of a vibration-reducing glove and the vibration transmissibility on the major substructures of the hand-arm system. The model-predicted results were also compared with the experimental data reported in two other recent studies. Some reasonable agreements were observed in the comparisons, which provided some validation of the developed models. This study concluded that the 5-DOF models are acceptable for helping to design and analyze vibrating tools and anti-vibration devices. This study also confirmed that the 5-DOF model in the z_h direction is acceptable for a coarse estimation of the biodynamic responses distributed throughout the major substructures of the hand-arm system. Some interesting phenomena observed in the experimental study of the biodynamic responses in the three directions were also explained in this study.