ABSTRACT We use the Illustris simulation to study the distributions of ellipticities and kinematic misalignments of galactic projections, as well as the intrinsic shapes and rotation of the simulated galaxies. Our results for the projections of galaxies display clear trends of an overall increase of kinematic misalignment and a slight decrease of ellipticity for fast rotators with increasing masses, while revealing no clear distinction between slow rotators of different mass. It is also found that the number of very slow rotators with large ellipticities is much larger than found in observations. The intrinsic properties of the galaxies are then analysed. The results for the intrinsic shapes of the galaxies are mostly consistent with previous results inferred from observational data. The distributions of intrinsic misalignment of the galaxies suggest that some of the galaxies produced by Illustris have significant rotation around their medium axes. Further analysis reveals that most of these galaxies display signs of non-equilibrium. We then study the evolution of the intrinsic misalignments and shapes of three specific Illustris galaxies, which we consider as typical ones, along the main progenitor line of their merger trees, revealing how mergers influence the intrinsic shapes and kinematics: the spin axis in general stays close to the shortest axis, and tends to quickly relax to such an equilibrium state within a few dynamical times of the galaxy after major perturbations; triaxiality and intrinsic flatness in general decrease with time, however, sometimes increases occur that are clearly seen to correlate with major merger events.