This paper is concerned with the pure displacement problem of planar linear elasticity. Our interest is focussed to a locking-free FEM approximation of the problem in the case when the material is almost incompressible. The approximation space is constructed using the Crouzeix-Raviart linear finite elements. Choosing a proper hierarchical basis of this space we define an optimal order algebraic multilevel (AMLI) preconditioner for the related stiffness matrix. Local spectral analysis is applied to find the scaling parameter of the preconditioner as well as to estimate the related constants in the strengthened C.B.S. inequality. A set of numerical tests which illustrate the accuracy of the FEM solution, and the convergence rate of the AMLI PCG method is presented.