In this paper, the free vibration of a completely clamped circular plate with a side crack and in contact with water on one side is investigated based on the Rayleigh-Ritz method. The plate is located at a hole of an infinite baffle and the crack whose depth is equal to the radius of the plate develops along the radial direction. First, the corner functions are introduced to describe the behavior of the cracks, and the Kirchhoff hypothesis is used during the calculation of the maximum strain energy and kinetic energy of the vibrating plate. Second, based on the hypothesis that the plate vibrates in small amplitude and the water is incompressible, inviscid and irrotational, the velocity potential is used to describe the motion of water and the added virtual mass increment expressed by the displacement trial functions is calculated by utilizing Green function method. Then, the characteristics matrix of the vibration system is obtained through Rayleigh-Ritz technique, and the natural frequencies and the corresponding modes are calculated. It is found that the reduction rates of eigenfrequencies due to influence of water decrease with the increasing of mode order but not monotonically, while the differences between dry and wet mode shapes increase with the increasing of mode order on the whole, and the influences of water on the symmetric modes and antisymmetric modes are different. Finally, the results are compared with those gained by numerical simulation and good agreement has been shown.