Several studies have investigated the feasibility of reducing the implementation cost of base isolation. In this optic, recycled rubber–fiber-reinforced bearings (RR–FRBs) represent a suitable solution for structures in developing countries. Such devices can be produced using simple manufacturing procedures at a limited cost with respect to conventional isolators. Full-scale tests on RR–FRBs featured energy dissipation values similar to those associated with high-damping natural rubber bearings (HDRBs). Equivalent viscous damping, ranging from 10 to 15%, resulted from testing of RR–FRBs, with poor degradation after cyclic loading. On the other hand, a sensible softening response, associated with the axial–shear interaction, which is much more significant compared to that exhibited by HDRBs, was observed. As a result, the numerical description of the cyclic behavior of the RR–FRBs appears to be more challenging than that of HDRBs. In past studies, simple bilinear hysteresis models were adopted to describe the cyclic behavior of low-cost rubber bearings, thus completely neglecting the P-delta effects which significantly influence the dynamic behavior of such bearings. In this paper, advanced hysteresis numerical models, able to capture the nonlinear response of RR–FRBs, were examined and properly calibrated using a powerful optimization technique, the differential evolution algorithm. Preliminary results of the numerical analyses, performed in OpenSees, were described and compared with those of experimental tests on low-cost rubber bearings. The findings of this study represent the first step of a characterization procedure aimed to provide an accurate representation of the dynamic behavior of these particular bearings. Obviously, additional studies are needed to compare results of response history analyses with those of experimental tests for real structures on RR–FRBs. In this optic, the present paper, along with further studies, could provide a new impulse for the application of low-cost rubber-based devices in current practice.