Many structural members of a ship hull are immersed in water or other kinds of liquid. The effect of such liquid on the free vibration of plates has been investigated by some people. Most bulkheads and walls of a ship hull are consist of stiffened plates, and it is very important to study how the stiffeners effect on the vibration of plates with such liquid-immersed condition. We developed a computer program for the vibration analysis of rectangular stiffened plates immersed in water. The analysis method is based on direct energy minimization theory by means of nonlinear programming. Besides, we adopted "projection method" to solve higher order vibration problems, and this method proved to be very useful. The calculated results showed good agreements with experimental results. In this paper we mainly confined ourselves to the descriptions of the analytical method and the comparison between calculated and experimental results. In the next paper, we will report on the estimation of virtual mass of stiffened plates vibrating in water.