The deformations and bending stresses of a mooring leg and a riser pipe of an assumed tension leg platform model are analyzed by two kinds of analytical methods under the condition of the severe irregular waves. One is a simulation in the time domain in which the drag term of the Morison's equation are left as the nonlinear term. The other is a linear response analysis in the frequency domain which is based on the linearization of the non linear drag term. From the comparison of the power spectral density functions and the related statistics derived from the two kinds of methods, the applicability and characteristics of the simpler latter method are discussed. In addition to these, the effects of bending on the structural responses of the mooring legs and risers of the tension leg platforms are studied.