The effects of the often neglected rotational components of strong earthquake ground motion on the response of two structural models are investigated. The first model approximates a structure by a massless column supporting a concentrated mass at its top and excited by incident plane waves in a homogeneous elastic half-space. The linear analysis, the effects of the vertical ground motion in the frequency term of the differential equation of motion neglected. The fourth order Runge-Kutta algorithm is employed to solve the nonlinear problem. The linear and nonlinear responses of the model for incident P, SV and Rayleigh wave excitations are studied. The transfer functions of the linear and nonlinear responses are investigated. The effects of rocking and vertical ground motions on the overall response of the model and on the response spectrum amplitudes are discussed.; The second model represents a three dimensional bridge with two spans erected on the elastic half-space and excited by incident body and rayleigh surface waves. The coupled-system of differential equations of motion is solved by the Runge-Kutta technique. The maximum relative rocking and twisting of the columns and the relative sliding of the girders is studied in the frequency domain. An application of the foregoing theory and examples of the response of a four span bridge model crossing a canyon and excited by transient earthquake excitations is presented.