Rotational ellipsoid generally used in geodetic computations. Triaxial ellipsoid surface although a more general so far has not been used in geodetic applications and , the reason for this is not provided as a practical benefit in the calculations. We think this traditional thoughts ought to be revised again. Today increasing GPS and satellite measurement precision will allow us to determine more realistic earth ellipsoid. Geodetic research has traditionally been motivated by the need to continually improve approximations of physical reality. Several studies have shown that the Earth, other planets, natural satellites,asteroids and comets can be modeled as triaxial ellipsoids. In this paper we study on the computational differences in results,fitting ellipsoid, use of biaxial ellipsoid instead of triaxial elipsoid, and transformation Cartesian ( Geocentric ,Rectangular) coordinates to Geodetic coodinates or vice versa on Triaxial ellipsoid.