Abstract: Two variational formulations for dynamic analysis of linear coupled fluid-solid interaction problems are presented in this paper. The linearized wave on free surface of fluid is considered in the formulations. The displacement in solid and the potential of velocity in fluid are used as the arguments of the first functional. The arguments in the second functional are the acceleration in solid and the dynamic pressure in fluid. A brief discussion on the use of the functi-onals in finite element methods is given at the end of the paper.