In this thesis, the seismic analysis of base isolated structures is carried out using a base coordinate relative to the inertial space that renders absolute dynamic response, which is fundamental in assessing base isolation. Moreover, the structure is modeled as an Euler-Bernoulli beam cantilevered on a massive basement. The isolation system is modeled as linear. The stochastic analysis is carried out in the frequency domain using a stationary Clough-Penzien spectral representation for the ground excitation. Standard deviations of the structure’s generalized coordinates and their second derivatives are obtained, which characterize the response, including stresses, of the structure. The effectiveness of base isolation can be evaluated by comparing the response of the isolated structure with the nonisolated counterpart. The results show that base isolation is highly effective in reducing the overall response of the structure. Additionally, it is found that the Clough-Penzien representation does not model adequately in the high frequency range. A modification of this model is proposed.