In this study, the assumed mode method using characteristic polynomials of Timoshenko beam is applied to the free vibration analysis for the stiffened plate of ship tank side in contact with water. The hydro-elastic effect of the fluid-structure interaction is considered by fluid velocity potential, derived from boundary conditions for fluid and structure, and utilized in the calculation of added mass matrix using assumed modes. To verify the validity and effectiveness of the presented method, free vibration analysis for the stiffened plates in contact with finite and infinite fluids have been carried out and its results were compared with those obtained by a general purpose FEA software.