Most 3-dimensional stress analysis is currently performed using the 8-noded linear and the 20-noded quadratic (serendipity) hexahedral elements. Recent experience with the quadratic plate/shell elements show that the 9-noded Lagrangian elements are superior to the 8-noded serendipity elements in applications to thin plate/shell flexure. Extension of this logic suggests that a 27-noded Lagrangian hexahedral element formulation with field-consistency corrections is needed for robust and reliable 3-D modelling of constrained media problems. In this paper we examine the field-consistency aspects involved in the formulation of such an element.