Abstract A new stiffness matrix which considers stiffness provided by hydrodynamic restoring force and yaw large angular displacements of a TLP, is proposed. The matrix is developed idealizing the platform as a rigid body moored by weightless cables to the sea bed, considering the nonlinearities produced by the largeness of the mooring system and global displacements, and a primary reference system at the gravity centre. Dynamic analysis is carried out considering random sea state through spectral analysis on time domain, wave forces are modelled trough Morison equation and through FNV theory to take into account wave diffraction effect. The proposed stiffness matrix is verified by comparing the dynamic responses obtained in this study with monitored responses reported in the literature. Moreover, dynamic responses are compared with previously two developed models for extreme conditions in three different regions of the Gulf of Mexico. These responses are obtained for a platform with dimensions similar to those of platforms used on the same site for the same purpose. Maximum differences about 21% are obtained for different pretensions.