In this work, both first harmonic and multiharmonic method are implemented to estimate the steady state response of wire rope isolators which is subject to arbitrary periodic excitation. First harmonic method is simple to implement in the sense of computer coding. In addition, when both frequency- and amplitude-controlled algorithms are formulated and are alternatively implemented, we would be able to obtain complete frequency-response curves including unstable solutions. While to determine the super harmonic resonant frequencies in the steady state, we resort to the discrete Fourier series (multi-harmonic) method. Finally, Galerkin/Levenberg-Marquardt Method is utilized to solve for a related optimization problem for those Fourier coefficients. Several numerical examples were examined to demonstrate the usage of these two methods.