Based on the principle of conservation of energy, analytical modelling of the energy response of continuous beam bridges with friction pendulum bearing (FPB) was carried out for foundation-induced vibrations. A three-dimensional finite element analysis of a multispan continuous concrete girder bridge with FPB was established using the nonlinear time-history method to verify the accuracy of analytical modelling. The influence of the friction coefficient and isolation period of the FPB on the energy response of isolated bridge was then investigated under multihazard source excitations (e.g., El Centro and Taft waves) with different dominant periods and durations. The variations of structural response energy, sliding displacement, energy dissipation ratio, and acceleration of the isolated bridges are plotted. The results of analytical modelling and finite element simulation show good agreement. In addition, there exist particular values of the friction coefficient and isolation period of FPB, for which the structural response energy of the isolated bridges attains the minimum value. The optimal parameters of FPB are greatly influenced by seismic waves, and the friction coefficient of FPB should be increased with the increase of seismic fortification intensity. In addition, the energy dissipation capacity of FPB used in isolated bridge is excellent.