Antenna structures used in electronic warfare, radar, naval, satellite, spacecraft systems encounter mechanical shock from various sources such as near miss under water explosion, pyrotechnic and ballistic shocks. Since most of the antenna structure has larger dimension in longitudinal direction and experience high frequency, high amplitude shock energy, geometric nonlinearity become crucial to predict dynamic behavior in real life. In this study, the antenna structure is modeled by Euler-Bernoulli beam theory including geometrical nonlinearity. The resulting partial differential equations of motion are converted into a set of nonlinear ordinary differential equations by using Galerkin's Method, which are solved by Newmark. The results for the linear system obtained from time integration and approximate methods such as Absolute Method, Naval Research Method, and Shock Response Spectrum Method (SRS) are compared to the nonlinear ones. Moreover, these results are compared with the ones obtained from commercial Finite Element software.