When the side-by-side offloading operation is carried out between FLNG and LNGC, strong hydrodynamic interactions will be induced by the two hulls. The weather vane effect of single point mooring system has attracted most focuses on the analysis of side-by-side configuration in head waves. Nevertheless, the influence of oblique waves on the motion responses of the side-by-side system cannot be ignored. This article investigates the hydrodynamic responses of the side-by-side system through theoretical analysis method and model testing method. Based on the 3-D potential theory and artificial damping-lid method applied on the gap surface between two vessels, the gap water resonance and linear hydrodynamic performances of side-by-side FLNG and LNGC are studied under oblique and head waves. Middle-field method is adopted to calculate the second-order hydrodynamic parameters, and reveal the influence of wave directions on the mean drift forces of both vessels. Investigation shows that the change of wave directions within a certain range does not influence the value selection of the free surface damping, while imposes influence on the mode and amplitude of gap water resonance. The variation of wave directions affects the shielding effect between FLNG and LNGC, and the motion responses of LNGC are greatly suppressed by FLNG under oblique waves. Besides, the main components of mean drift forces on the two vessels change accordingly under different wave directions.