Rubber mount modeling in multibody simulation is crucial for accuracy in this type of calculation, and despite its importance, they are often underestimated in terms of modeling. The present work aims to develop and implement a finite element model suited for rubber behavior in large deformations, and apply hyperreduction techniques to evaluate the possibility of a direct implementation into a multibody simulation, or to generate a novel family of joint models. The article begins with the development and implementation of the material behavior, then a brief explanation on the implemented finite elements routine along with the hyper-reduction method used. An analysis of the results and an insight of future developments closes the article.