Abstract: The frequency-domain-analysis methods for hydroelasticity of very large floating structures are discussed and reviewed. The dry mode method, the wet mode method and the direct method are presented. For the dry mode method, five kinds of mode functions are introduced, and convergences of the dry mode methods based on the five mode functions are examined. Computation cost and computer memory requirement of hydrodynamic analytical methods are discussed as well. Some higher speed and lower memory requirement methods are also introduced. A multipole expansion method in the cylindrical coordinate system is implemented in the higher order boundary element approach to accelerate the computation and decrease the memory requirement. The free-term coefficient and the Cauchy principal value integral in the integral equation is computed by their corresponding direct methods.