The present study aims to investigate the dynamic properties of a novel isolation system composed of separate rubber and wire isolators. The testing program comprised pure compressive, pure-shear, compressive-stress dependence, and shear-strain dependence tests that used full-scale test specimens according to ISO 22762-1. A total of 22 test specimens were fabricated and investigated. Among the tests, the pure compressive test was a destructive test that reached up to the failure stage, whereas the others were nondestructive tests before the failure stage. Similar to the pure-shear test, at each compressive-stress level in the compressive dependence test or at each shear-strain level in the shear-strain dependence test, the cyclic loading was conducted for three cycles. In the nondestructive tests, examination of the dynamic shear properties in the X-direction was independent of the Y-direction. The test results revealed that the increase in the shear strain increased the energy dissipation but decreased the damping ratio, whereas the increase in the compressive stress increased the damping ratio. In addition, a macro model was developed to simulate the load-displacement response of the isolation systems, and the prediction results were consistent with the experimental results.