Abstract The offshore structures are flexible systems subjected to various types of loadings. The heavy gravitational loads on the top decks, wind and water wave pressures acting on the platforms are transferred to the soil through the piles or mat foundations. Under the vibration, the variation in the pore pressures induces additional effects on the embedded part of the piles. The effect of the soil-structure interaction on the dynamics of the structure is taken into account as the deformations of the soil caused by the motion of the structure which in turn modify the response of the structure. The effect of the axial forces, within the individual members, on the vibration of the structure is included in the formulation. The dynamic stiffness matrix of the members are developed by considering the actual mass distribution and the effect of the axial force of the members. For the members embedded into soil, the soil reactions and the skin frictions are also considered as continuously varying over the members. Therefore, the equations of motion are satisfied along any infinitesimal element of the members. The new formulation is introduced in the general purpose computer code STDYNL, then the sensitivity of the overall dynamic response of the deep water platforms to the variation of the soil characteristics and to the effect of the axial forces of the members are investigated.