In this paper, a hybrid stress 12-node brick element is presented Its assum
ed stress field is derived by first examining the deformation modes of a ge
ometrically regular element and then generalizing to other element configur
ations using tensorial transformation. The total number of stress modes is
30 which is minimal for securing the element rank. To reduce the computatio
nal cost associated with the fully populated flexibility matrix, the admiss
ible matrix formation is employed to induce high sparsity in the matrix, Po
pular beam bending benchmark problems are examined. The proposed elements d
eliver encouraging accuracy.