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In the paper, a three-axis power transmission system is modeled mathematically and simulated by software. In mathematically method, a system consisting of three flexible shafts with different rotation axis which connected through two universal joints is investigated via a three degree-of-freedom model. The stability is analyzed by means of a monodromy matrix technique. This is verified by comparing the results with dynamic analytical software AdamsView simulation and the results of the previous research. Then, the effects of rotational velocity, non-aligned angles, shaft's properties (stiffness and damping) on the stability are investigated. Finally, the stability charts constructed on various parameters is presented. It is observed that decreasing shaft stiffness and universal joint angle due to more stability, while decreasing shaft damping has the opposite effect.