The finite element discretization of nearly incompressible hyperelasticity problem for modelling soft-tissue mechanics leads to a large-scale nonlinear system, which is typically linearized using Newton?s method and solved iteratively. The stiffness matrix generated at each Newton iteration is a highly ill-conditioned linear system and the large number of degrees of freedom in realistic simulations often impact the efficiency of standard linear solvers, making effective and robust preconditioning essential. In this talk, I will present a robust condition number estimate for the performance of two-level overlapping Additive Schwarz preconditioners with the Extended Nicolaides coarse space for the above problem and also illustrate a few numerical results.