In this talk, we shall present preliminary results based on the Arnold-Falk-Winther mixed finite element for the linear elasticity. The method introduces the stress tensor, the displacement field, and the anti-symmetric part of the strain tensor as independent variables. The formulation is based on the variant of the Hellinger-Reissner variational principle which weakly imposes the symmetry conditions on the stresses. The equations will be reformulated in terms of differential forms using the Finite Element Exterior Calculus. The simplest low order compatible discretization will be chosen. Numerical results will be shown on various planar linear elasticity problems. Special attention will be paid to the incompressible limit as the Poisson’s ratio tends to $1/2$.