In recent years, high damping rubbers (HDRs) have been extensively employed for seismic isolation of bridges or buildings because they permit to obtain bearings with low horizontal stiffness and moderately high dissipation capacity, thus increasing the vibration period and dissipation capacity of the structures. HDR is obtained by adding a filler to the natural rubber in order to improve some of its properties in terms of strength, stiffness, as well as dissipation capacity. The addition of the filler also induces a nonlinear behaviour in the HDR. In particular, the transient behaviour tends to rise up and there is a progressive loss of rigidity due to the damage of the internal microstructure. In the case of a cyclic load test with constant amplitude this phenomenon involves the first load cycles and progresses up to stabilization of the damage (the effect is known as ‘scragging'). In general, the material response and damage evolution depends strongly on the load history and particularly on the maximum deformation experienced along the path. This phenomenon is known as the Mullins effect. It should also be noted that the initial properties of the material are recovered in a sufficiently short time so that variations of the stiffness and dissipation capacity due to the Mullins effect always influence the seismic response. The present work intends to study the consequences of such non-linear behaviour in the seismic response of bridges isolated with HDR bearings. For this purpose, the response of a realistic bridge model under seismic inputs with different characteristics and different intensities is analyzed  by using a constitutive model of the HDR, previously developed by the authors, able to describe the inelastic and strain dependent behaviour of the rubber and the damaging effects. The obtained results are compared with those obtained by adopting simple linear models suggested by several seismic codes.