In a previous paper, incremental transfer stiffness coefficient method was developed in order to analyze the periodic steady-state vibrations of a large-scale structure having locally strong nonlinear elements. By this method, the computation cost of this method can be reduced markedly from the iterative computation process of approximate solution. In this paper, an algorithm based on the presented method is formulated to analyze the longitudinal, flexural and torsional coupled vibration of a three-dimensional tree structure supported by nonlinear base support elements. In addition, stability analysis using a reduction model is applied to the periodic solution obtained for the three-dimensional tree structure. The validity of the incremental transfer stiffness coefficient method and the method of stability analysis using the reduction model for three-dimensional tree structures is confirmed by the numerical computational results.