Summary: This paper presents a natural nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the pure displacement Navier-Lamé equations. The convergence rates are robust with respect to the Lamé parameter \(\lambda \to \infty\) in the sense that all constants in the quasi-optimal convergence rate stay bounded for almost incompressible materials and so the Stokes equations are covered by our analysis in the limit \(\lambda = \infty\).