The projected properties of triaxial generalization of the modified Hubble mass models are studied. These models are constructed by adding the additional radial functions, each multiplied by a low-order spherical harmonic, to the models of [Chakraborty, D.K., Thakur, P., 2000. MNRAS 318, 1273]. The projected surface density of mass models can be calculated analytically which allows us to derive the analytic expressions of axial ratio and position angle of major axis of constant density elliptical contours at asymptotic radii. The models are more general than those studied earlier in the sense that the inclusions of additional terms in density distribution, allow one to produce varieties of the radial profile of axial ratio and position angle, in particular, their small scale variations at inner radii. Strong correlations are found to exist between the observed axial ratio evaluated at 0.25R e and at 4R e which occupy well-separated regions in the parameter space for different choices of the intrinsic axial ratios. These correlations can be exploited to predict the intrinsic shape of the mass model, independent of the viewing angles. Using Bayesian statistics, the result of a test case launched for an estimation of the shape of a model galaxy is found to be satisfactory.