This paper investigates the non-linear inelastic seismic response of existing single-span simply supported bridges having bearings which can remain stable and slide after their anchor bolts are ruptured. A simplified equivalent model is developed for the inelastic analysis of these single-span simply supported bridges. Non-linear inelastic time-history analyses are conducted for various acceleration inputs. It is found that narrower bridges with longer spans may have considerable sliding displacements and fall off their supports if adequate seat width is not provided. It is also found that for the same ratio of friction coefficient to peak ground acceleration, the sliding displacement of a structural system is linearly proportional to the amplitude of the peak ground acceleration beyond a certain threshold value. This is also demonstrated analytically from an energy approach point of view. The distribution of the energy content of an earthquake, which is related to its velocity time history, can be an indication of the propensity of an earthquake to cause high sliding displacement Ground motions with high frequency content or high A(p)/V-p ratio may produce smaller sliding displacements than ground motions with relatively lower A(p)/V-p ratios.