High-damping natural rubber (HDNR) bearings are extensively employed for seismic isolation of structures because of their low horizontal stiffness and high damping capacity. Filler is used in HDNR formulations to increase the dissipative capacity, and it induces also a stress softening behaviour, known as the Mullins effect. In this paper, a wide experimental campaign is carried out on a large number of virgin HDNR samples to better investigate some aspects of the stress softening behaviour, such as the direction dependence and recovery properties, and to characterize the stable and softening response under different strain histories. Test results are also used to define a model for simulating the response of HDNR bearings in shear that adv...