Abstract A coupled thermo-mechanical 3D finite element model is developed to simulate the cogging-down rotary swaging (RS) processing of pure magnesium square billet in this paper. Through simulation, the effects of high-frequency pulse stroking, special to RS, on the distributions and histories of different field-variables such as stress, strain, temperature and so on are clarified. The effect of the cogging-down RS on the subsequent RS passes is also analyzed. It is shown that the strain of each node increases stepwise with pulse stroking. The equivalent strain of nodes at the corner of the square billet is much higher than that at the center by 1.48. The stresses fluctuate periodically with the pulse stroking. The axial component σ z of the residual stress at the corner of the cogging-down RS bar is as high as 32 MPa that it becomes one of the main factors causing the transverse surface crack in the subsequent RS passes. The temperature rising owing to the heat translation from plastic deformation energy is only 1 °C in the cogging-down RS. Compared the calculated results with experimental data, the consistency is demonstrated.