- Arterial wall can be modeled by a quasi-incompressible, anisotropic and hyperelastic equation that allows large deformation. Most existing nonlinear solvers for the steady hyperelastic problem are based on pseudo time stepping, which often requires a large number of time steps especially for the case of large deformation. It is also reported that the quasi-incompressibility and high anisotropy have negative effects on the convergence of both Newton’s iteration and the linear Jacobian solver. In this paper, we propose and study a nonlinearly preconditioned Newton method based on nonlinear elimination to calculate the steady solution directly without pseudo time integration. We show numerically that the nonlinear elimination preconditioner accelerates Newton’s convergence in cases with large deformation, quasi-incompressibility and high anisotropy.