The restoring stiffness, which couples displacements and deformations, plays a very important role in hydroelastic analysis of marine structures. The problem of its formulation is quite complex and is still discussed in relevant literature. In this paper, the recent formulations of restoring stiffness are correlated and analyzed. Due to some common terms of the restoring and geometric stiffness, the unified stiffness is established and compared with the complete restoring stiffness known in relevant literature. It is found out that the new formula deals with more terms and that under some assumptions, it is reduced to the known complete restoring stiffness. The unified stiffness constitution is analyzed through derived analytical formulae for prismatic pontoon. Its consistency is checked for the rigid body displacements. Also, numerical results of the hydroelastic response of segmented barge are correlated with available model test results. Some issues, that are important for practical implementation in the hydroelastic code for flexible structures, are described.