The aim of this study is to present a general model with variable coefficients corresponding to some structural elements such as beam, string, bar, and rod. To solve general model with variable coefficients, a different solution procedure combining a method of multiple scales (MINIS) and a finite difference method (FDM) is presented in this study. This technique provides an advantage in the numerical solution of the structural element model containing any discontinuity and in its dynamical analysis by perturbation method. Furthermore, two problems including discontinuity are considered to show the accuracy of the method presented. The comparisons of the numerical results obtained from the proposed method and classical method are introduced.