In this paper we investigate the performance of the nonconforming linear strain tetrahedron element introduced by Hansbo (Comput Methods Appl Mech Eng 200(9–12):1311–1316, 2011; J Numer Methods Eng 91(10):1105–1114, 2012). This approximation uses midpoints of edges on tetrahedra in three dimensions with either point continuity or mean continuity along edges of the tetrahedra. Since it contains (rotated) bilinear terms it performs substantially better than the standard constant strain element in bending. It also allows for under-integration in the form of one point Gauss integration of volumetric terms in near incompressible situations. We combine under-integration of the volumetric terms with houglass stabilization for the isochoric terms.