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In this paper, the solution and model of rigid-liquid coupled dynamics state equations of spacecraft with multiple liquid-filled cylindrical tanks in low-gravity environment are mainly studied. Firstly, the carrier motions equations of a representative point in liquid-filled cylindrical tank in spacecraft are deduced, and the carrier potential function equations of liquid in the tank are given according to wall boundary conditions. The complex dynamic boundaries conditions on curved free-surface under low-gravity environment are transformed to general simple differential equations by means of Fourier-Bessel series expansion method. The dynamic state equations for coupled rigid-liquid spacecraft system are presented, in which, the state vectors of equations consist of the modal coordinates of relative potential function and the modal coordinates of wave height. The formulas of coupled sloshing forces and coupled sloshing moments are obtained by integrating. Then the dynamic state equations of coupled motion of main body are deduced using the Lagrange's equations in terms of general quasi-coordinates. Correspondingly, the rigid-liquid coupled dynamics state equations of whole systems of spacecraft are obtained. Lastly, a modularized calculation code based on the present method is programmed. The influences of layouts of multi-tanks and driving mode on the dynamics performance of coupled rigid-liquid system are studied. Consequently, the validity of the presented methods and the computer program are verified. [ABSTRACT FROM AUTHOR]