The rigid body swing is an important problem for steel catenary risers (SCRs). In addition to many other important issues, the transverse flow direction response is studied in this paper. By extending the load terms of the large deflection slender beam equation, the load of suspension point in the z direction, Morison and rigid body swing are superimposed on the beam equation. On the basis of the above work, a Cable3d subroutine is written to complete the task. Then the structural response is simulated and verified by the Lissajous phenomenon and spectral phase analysis. On the basis of verification, the response is analyzed from an angle of three-dimensional space and the influence coefficient is adopted to evaluate the effect of rigid body swing. The importance of loads is determined by spectral analysis. Phase curve and the change of vibration direction are analyzed by higher orders of frequency. The results show the verification of Lissajous and spectral phase analysis are feasible. The analysis of the spatial response shows the vibration direction of the 140th node is in the same direction as the rigid body swing vector, so the interaction is relatively of more intensity and the influence coefficient is relatively larger. This influence interval of rigid body swing displacement statistical analysis is −0.02 to 0.02 and the effect is weak. The spectrum analysis indicates there is no resonance between the main load and the bending vibration, and the analysis also shows the main influence load of the transverse flow response in this paper is the top load in the z direction. According to phase analysis, the load has a high order effect on the spectral phase curve of the structure. This paper has drawn a conclusion that rigid body swing has limited effect on transverse flow response, however, it has a relatively strong impact on the middle region of the riser, so it plays an influential role on the safety of the riser to some extent. The key point for this paper is to provide qualitative standards for the verification of rigid body swing through Lissajous graphs, which are central factors to promote the development of rigid body swing. It is hoped that the above research can provide some reasonable suggestions for the transverse flow response simulation of the steel catenary riser.