The present paper introduces a mixed stress-displacement method for linear elastic- ity as an extension of the work performed by Christiansen [Numer. Math., 119 (2011), pp. 613–640] for computational relativity. Moreover, we establish self-adjointness in a special sense and perform numerical simulations to assess the relevance of the method, including comparison with the recent TDNNS [A. Sinwel, A New Family of Mixed Finite Elements for Elasticity, Ph.D. thesis, Linz Uni- versity, 2009], [A. Pechstein and J. Scho ̈berl, Math. Models Methods Appl. Sci., 21 (2011), pp. 1761– 1782] mixed formulation. Extensions to higher order approximations and nonlinear elasticity are also introduced.