Using finite element method, free vibration of very large circular floating structures is investigated based on the first order shear deformation theory. The very large floating structure is modeled as an elastic plate with free edges. The free vibration of a circular plate in contact with air (the dry plate) is investigated and the natural frequencies and mode shapes of the plate are determined using a code written in MATLAB as well as with ABAQUS software. Then a circular plate in contact with water (the wet plate) has been considered. Using ABAQUS software, The effect of the presence of water on vibrating plate is reflected by plate added mass. The good agreement between the present results with those of previous studies approves the accuracy of the finite element method for free vibration analysis of very large floating structures.