A finite element formulation modelling hyperelastic quasi-incompressible rubber-like materials (elastomers) is developed which takes into account large displacements and large elastic strains as well as inelastic effects. The capacity of laminated rubber-like materials to support high loads in compression and large displacements in shear is the principal reason for their use in devices for seismic base isolation of structures. The energy-dissipation capacity of these devices is increased by using high damping rubber, which is an elastomer incorporating carbon black particles, or having lead-plug insertion. The Ogden strain energy function has been used as a basis for the material model implemented in a total Lagrangian formulation, the strain being decomposed into its deviatory and volumetric parts and the pressure variable being condensed at element level. Mooney-Rivlin and neo-Hooke strain energy functions can also be used by simply changing the parameters of the model. The stress-strain hysteresis, which appears when these devices are subjected to dynamic or quasi-static cyclic loads, has been modelled by frequency dependent viscoelastic and plastic constitutive models. The bearings have been modelled by means of an equivalent single element capable of describing the composite behaviour of the actual isolation system. The proposed model is validated using available experimental results and it is proved to be a powerful tool in dealing with different bearings. Finally, results for a six-storey base isolated building subjected to the El Centro earthquake are given.