Selection of appropriate hyperelastic and viscoelastic material models in Finite Element Analysis (FEA) is essential for accurate simulation of the lateral load–displacement behaviour of Fiber Reinforced Elastomeric Isolators (FREI). However, there are limited studies on the experimental determination of viscoelastic and hyperelastic properties of the elastomers used in FREI. The present study aims to experimentally determine the viscoelastic and hyperelastic properties of elastomers and use these parameters in FEA to accurately predict the mechanical behaviour of FREI. Uniaxial tension tests are conducted to obtain the hyperelastic constants, which describe the non-linear elastic response of the material. Additionally, Dynamic Mechanical Analyzer (DMA) tests are performed to determine the viscoelastic constants, which capture the time-dependent behaviour of the material. These experimentally determined material constants are then used to derive the coefficients for the three-term Ogden model and the two-term Prony shear model. These parameters are used for representing the viscoelastic and hyperelastic properties of elastomers in the FEA of Unbonded Fiber Reinforced Elastomeric Isolators (U-FREI). In order to validate the FEA results, a comparison is made between the force–displacement hysteretic response acquired from the simulations and those obtained from the experimental tests. The numerical force–displacement hysteresis loops of U-FREI are in close agreement with those obtained from the experimental study, which demonstrates the accuracy and reliability of the FEA model.