The scrap tire rubber pad (STRP) made by natural or synthetic rubber and high strength reinforcing cords exhibits substantial vertical stiffness and horizontal flexibility, and these properties can be regarded as suitable for seismic isolators for structures. The use of environmentally burdensome scrap tires as STRP isolators might be convenient as an efficient and low-cost solution for the implementation of aseismic design philosophy for low-to-medium rise buildings, especially in developing countries. Finite element analyses of unbonded square and strip-shaped STRP isolators subjected to a combination of axial and lateral loads are conducted to investigate its lateral deformation performance under seismic loading. The rubber of the isolator is modelled with Mooney-Rivlin hyperelastic and Prony viscoelastic materials, including the Mullins material damage effect. The influence of the length-to-width ratio and bearing height on the isolator performance is assessed in terms of the force-displacement relationship, horizontal stiffness, damping, and isolation periods. It is shown that the dependence of stiffness on the length-to-width ratio is significant in the longitudinal direction and minor in the transverse direction. The STRP isolators following the proposed design criteria are shown to satisfy the performance requirement at different levels of seismic demand specified by the ASCE/SEI 7–2010 seismic provisions.