The applications of direct treatment and discretizations of non-linear dynamics are investigated in this paper. These two approaches are applied to attack the primary resonance of the nth mode of suspended cables. These lead to obtain the second order approximate solutions and the associated frequency-response curves. The results obtained with these two approaches are compared. And the differences of these results are discussed. Finally, the results are obtained that the discretization of nonlinear dynamic of non-symmetric structure may lead to erroneous results.