This paper addresses the accurate modeling of the behavior of a thin layer of natural rubber subjected to large deformations. Such a system presents a non-linear viscoelastic behavior similar to many biological soft tissues. The proposed model uses an spring-mass system, and considers a non-linear evolution of the reaction forces of the membrane,as well as viscous and Coulomb friction. In the model, the elasticity coefficient of the springs has an exponential dependence of its elongation. Three experimental tests validate the proposed model, which reaches a real-time performance using an implicit integrator