The second generation intact stability criteria are finalized by the International Maritime Organization (IMO) in 2022. For the application of the criteria in the ship industry, the development of the domestic CAE software demands a reliable mathematical model for direct assessment of pure loss of stability. It aims at a mathematical model with sufficient accuracy and practicability for direct assessment of the pure loss of stability for ships in regular quartering seas. Firstly, a nonlinear time-domain motion mathematical model with six degrees of freedom (6-DoF) coupling of surge-sway-heave-roll-pitch-yaw is established by referring to the standard manoeuvrability MMG model, surf-riding/broaching mathematical model and parametric rolling prediction model. Secondly, the time-domain heave and pitch and the time-domain diffraction and radiation forces are obtained by transferring from frequency-domain to time-domain, and the amplitude and initial phases are obtained by a strip method with consideration of the ship speed. Then, the Froude-Krylov(F-K) force and the hydrostatic force in the directions of surge, sway, roll and yaw are calculated by integrating along the instantaneous wet surface, considering the change in the instantaneous relative position of the ship and the waves due to the 6-DoF oscillations. Finally, the numerical predictions of the pure loss of stability for an ONR tumblehome ship in quartering seas are compared with the experimental results. It is verified that the 6-DoF mathematical model can be used to directly assess the pure loss of stability of ships in quartering seas. It is confirmed that the coupled forces of sway and yaw in the roll direction is also an important reason for the large-scale roll instability due to the pure loss of stability.