In this paper, analytical simulations of the steel-laminated elastomeric bearing (SLEB) using a three-dimensional (3D) finite element model incorporating material, geometric nonlinearities, and a frictional contact algorithm in LS-DYNA code is conducted. In order to simulate the nonlinear responses of the elastomeric bearing under the compression and shear, a hyperviscoelastic rubber model such as The MAT-77-H (MAT-HYPERVISCOELASTIC-RUBBER) in LS- DYNA code is adopted. Based on the proposed material model for the SLEB, the interaction effects of the SLEB under compression, bending, and torsion are analyzed. Analytical results are compared with the test results of the SLEBs. A set of material parameters is proposed for 3D FEM analysis of SLEBs. The proposed material model demonstrates its accuracy.