Due to the effect of fluid viscosity exerted on the motions for a cylindrical structure, a series of complex changes will occur in the motion variations, especially for the motion of single degree of freedom. However, the computation accuracy of traditional computing methods has been limited, with no thought for the fluid viscosity. In this paper, a three-dimensional numerical wave tank is established based on the theory of viscous fluid mechanics. Firstly, a series of convergence analysis of different grid resolutions are carried out, and the parameters of numerical models are optimized. After that, taking the fluid viscosity into consideration, the heave motions of different cylinders with various sizes are investigated via the optimized models. Meanwhile, the equation of wave-cylinder coupling movement is established based on the potential flow theory and linear gravity water wave theory. And the analytical solution is obtained. Finally, through comparing the analytical solution and the numerical results, the basic moving laws of float has been validated and the variations of heave motion of cylindrical structures is analyzed systematically.