The understanding of the seismic response of fault-crossing bridges is still insufficient despite the increasing interest in this subject by earthquake engineers over the past two decades. This dissertation focuses on (a) developing and validating a simple method for generating across-fault seismic ground motions for the analysis of bridges crossing strike-slip faults, (b) investigating the sensitivity of the seismic response of bridge structures crossing strike-slip faults to different parameters and conditions by means of nonlinear response history analysis (NLRHA), and (c) evaluating the accuracy of the fault rupture-response spectrum analysis (FR-RSA) method against NLRHA in estimating the peak response of bridges crossing strike-slip faults for different fault crossing conditions.The effect of ground motion filtering on the dynamic response of a seismically isolated bridge with and without fault crossing considerations is first investigated. The results indicate the importance of permanent ground displacement on the dynamic response of spatially extended engineering structures crossing fault rupture zones. A simple and effective method for generating across-fault seismic ground motions for the analysis of ordinary and seismically isolated bridges crossing strike-slip faults is then proposed. Two loading functions are introduced based on pulse models available in the literature to represent the coherent (long-period) components of ground motion across strike-slip faults. A comprehensive methodology is presented for selecting the input parameters of the loading functions based on empirical equations and practical guidelines. An analysis procedure for bridge structures crossing strike-slip faults is introduced based on the proposed method for generating across-fault ground motions and the parameter selection methodology for the loading functions. Moreover, a parametric study of ordinary and seismically isolated bridges crossing strike-slip faults is presented by performing NLRHA using the proposed loading functions and by varying their parameters according to the aforementioned methodology. The sensitivity of the displacement demands of the analyzed bridges to each parameter of the loading functions is examined.To investigate the effects of fault crossing conditions and structural properties on the seismic response of bridge structures crossing strike-slip faults, a parametric study of ordinary and seismically isolated bridges is presented by performing NLRHA using actual near-fault ground-motion records from earthquakes of different magnitudes and by varying the fault crossing angle, fault crossing location, pier height, and span length. In addition, the effects of seismic excitation polarity and number of ground-motion components on the seismic response of the analyzed bridges are examined. Finally, the adequacy of the FR-RSA method for estimating the peak response of ordinary and seismically isolated bridges under different fault crossing conditions is investigated. Such an investigation involves examining the effects of modal combination rule, number of modes, damping ratio, and mode type on the peak response of bridge structures estimated from the FR-RSA method.