Two partially filled tanks fixed on rectangular barge floating in variable bathymetry is studied based on the linearized potential theory in the frequency domain. The internal sloshing motion is simulated by linearized superposition of natural sloshing modes. The motion of barge is solved by matching eigenfunctions expansion in the external fluid domain. The computational model is verified by experimental results. Coupling sway and roll motions of floating body with different filling levels are compared. The effects of both inclined bottom with different slopes and hump-shaped bottom with different heights are analyzed. Viewing from the results, coupling sway and roll motions of floating body are significantly affected by the shapes of bottoms.