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In this paper, we study the construction of low-degree robust finite elementschemes for planar linear elasticity on general triangulations.  Firstly, we present a low-degree nonconforming Helling-Reissner finiteelement scheme. For the stress tensor space, the piecewise polynomial shapefunction space is $$ {\rm span}\left\{\left(\begin{array}{cc}1&0\\ 0 &0\end{array}\right),\left(\begin{array}{cc}0&1\\ 1 &0\end{array}\right),\left(\begin{array}{cc}0&0\\ 0 &1\end{array}\right),\left(\begin{array}{cc}0&x\\ x &0\end{array}\right),\left(\begin{array}{cc}0&y\\ y &0\end{array}\right),\left(\begin{array}{cc}0&x^2-y^2\\ x^2-y^2 &0\end{array}\right)\right\}, $$ the dimension of the total space isasymptotically 8 times of the number of vertices, and the supports of the basisfunctions are each a patch of an edge. The piecewise rigid body space is usedfor the displacement. Robust error estimations in $\mathbb{L}^2$ and broken$\mathbf{H}({\rm div})$ norms are presented.  Secondly, we investigate the theoretical construction of schemes withlowest-degree polynomial shape function spaces. Specifically, aHellinger-Reissner finite element scheme is constructed, with the local shapefunction space for the stress tensor being 5-dimensional which is of the lowestdegree for the local approximation of $\mathbf{H}({\rm div};\mathbb{S})$, andthe space for the displacement is piecewise constants. Robust error estimationsin $\mathbb{L}^2$ and broken $\mathbf{H}({\rm div})$ norms are presented forregular solutions and data.

Low-degree robust Hellinger-Reissner finite element schemes for planar linear elasticity with symmetric stress tensors