Fluid-structure interaction (FSI) has resulted in both complex applications and computing algorithmic improvements. The aim of this paper is to develop a better understanding of the fluid-structure interaction behaviour and the numerical coupling methods which can be used in analysing the FSI problem of a multi-physics nature computationally. There are two different systems in partitioned methods for coupling the fluid and structural domains which use strong and weak couple algorithms. Numerical results have been obtained on the hypothetical models for the close and open-spillways concrete gravity-dam. The two-way coupling partition method has been applied to the dynamic velocity flow and pressure using the ANSYS FEA software. A close comparison between the weak and strong coupled systems of two-way partitioned method has been made for the consideration of both close and open-spillways concrete gravity-dam.