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The hybrid stress method has demonstrated many improvements over conventional displacement-based elements. A main detraction from the method, however, has been the higher computational cost in forming element stiffness coefficients due to matrix inversions and manipulations as required by the technique. By utilizing special transformations of initially assumed stress fields, a spanning set of orthonormalized stress modes can be generated which simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived. The developed methodology is demonstrated using several selected 2-D quadrilateral and 3-D hexahedral elements. Finite element analysis