Abstract. Determination of the intrinsic shape and the orientation of individual elliptical galaxies is an important problem. The statistical method to determine the shape and orientation was developed by Statler and his coworkers. These authors use the photometric, as well as, the kinematical data of the galaxies. As the numbers of galaxies with good photometry are many more as compared to those with good kinematics, we attempt the shape estimates using photometric data alone. We determine the intrinsic shapes and orientations of the light distribution of galaxies by combining the pro.les of photometric data from the literature with triaxial models. The intrinsic shapes and orientations are given by a Bayesian probability distribution. The likelihood of obtaining the data from a model is a function of the parameters describing intrinsic shape and orientation. We apply the method to infer the shape and orientation of a galaxy, using the ellipticities and the difference in the position angles at two suitably chosen points from the pro.les of the photometric data. The expectation values (< q₀ >, < q _∞ >, < |T_d | >) and most probable values (< q_0P, < q _{∞ P} >, < |T_dP | >) constitute a summary of the shape of NGC 3379, we .nd < Q_0P>= 0.93, < q _∞ P > = 0.78, <|T_dP|> = 0.03, < q ₀ > = 0.88, q _∞ = 0.72 and < | T_d| >= 0.29. These can be compared with the values < cL > = 0.75, | T _dP| = 0.03, cLP = 0.87, TmP = 0.0, reported in Statler (1994, ApJ, 425, 500; hereafter S 94). The expected as well as the most probable values of the short to long axial ratios of our calculation agree extremely well with the values in S94. This agreement establishes our methodology, quite .rmly. We also .nd that the orientation of NGC 3379 is not well constrained. This is again in agreement with the results obtained by Statler (1994, Astr.J., 108, 111) We .nd that the position angle difference plays the crucial role in orientation estimates. Orientation of the elliptical galaxies with position angle difference ≥ 40.0 are well constrained. The results of shapes and orientations of other galaxies can also be compared with the values reported by other workers.