A family of triaxial Stackel potential-density pairs is introduced. Wi
th the help of a Quadratic Programming method, a linear combination of
potential-density pairs of this family which fits a given projected d
ensity distribution can be built. This deprojection strategy can be us
ed to model the potentials of triaxial elliptical galaxies with or wit
hout dark halos. Besides, we show that the expressions for the Stackel
triaxial density and potential are considerably simplified when expre
ssed in terms of divided differences, which are convenient numerically
. We present an example of triaxial deprojection for the galaxy NGC 51
28 whose photometry follows the de Vaucouleurs law.