From the text: We describe a stable mixed finite element method for linear elasticity in three dimensions. This answers an assertion of

*D. N. Arnold* [Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press. 137–157 (2002;

Zbl 1023.65113)]: ‘Four decades of searching for mixed finite elements for elasticity, beginning in the 1960s, did not yield any stable elements with polynomial shape functions’. First

*D. N. Arnold* and

*R. Winther* [Numer. Math. 92, No. 3, 401–419 (2002;

Zbl 1090.74051)] gave stable elements for a two-dimensional version of the problem, and remarked that the method of construction works in both two and three space dimensions, but for simplicity the discussion was limited to the two-dimensional case.