In collaboration with Eurocopter, we have developed a reduction model strategy to the simulation of laminated rubber-bearings. In the context of a varational formulation for nearly incompressible hyperelastic bodies, we have carried out reduced finite elements. Via an enrichment of the unknown fields, we condensed the direction of length and thus reducing the computing size (and therefore the computing time). From the results of numerical tests (compared to the numerical response of models of reference) we have illustrated the reliability and the performances of the proposed method. These comparisons are done both on the global response (effective stiffness, resulting loads) and the local response (stress fields, ...). As an application, we have first used this method together with a continuation strategy to study the structural stability of laminated bearing structures. Then we have realized an extension of this method for dissipative materials (visco-hyperelastic) with a Kelvin-Voigt model. Finally, we have analysed the response of a composite beam (elastomer and glass or carbon unidirectional fibers).