The translational-torsional dynamics model of planetary gear transmission systems has been established through the lumped parameter method. The natural frequencies and vibration modes have been obtained using this model. The distribution of natural frequencies has been systematically described. The vibration modes have been classified and characterized. A method for quantifying the influence of system parameters on the natural frequency of planetary gear transmission been proposed. The effects of support stiffness, meshing stiffness and torsional stiffness on the natural frequencies and vibration modes of planetary gear transmission system have been quantitatively evaluated. The sensitivity of each stiffness to the inherent characteristics of the system is determined. The results have demonstrated that the support stiffness of sun, planet and carrier have significantly influenced on the low-order natural frequency. Ring support stiffness and meshing stiffness have exhibited substantial effects on specific high-order natural frequencies. Torsional stiffness has exclusively affected central components’ torsional vibration modes corresponding to high-order frequencies. Internal meshing stiffness has primarily governed ring/planet vibration frequencies, while external meshing stiffness has predominantly influenced sun/planet vibration frequencies. These findings have established theoretical foundations for enhancing dynamic performance through resonance avoidance and parameter optimization in planetary gear transmissions.