Using density functional theory (DFT) calculations, we have studied structural models of graphite fluorides for five fluorine compositions; C(1)F (CF(1)), C(2)F (CF(0.5)), C(3)F (CF(0.33)), C(4)F (CF(0.25)), and C(16)F (CF(0.0625)). For each composition, we considered several possible structural models and calculated heat of formation relative to the pristine graphite and F(2) molecule. We also simulated X-ray diffraction patterns for each structural model and compared those with experiments. We find, in agreement with earlier experiments, that the most stable structure of the C(1)F (CF(1)) has an infinite array of trans-linked cyclohexane chairs of covalent C-F bonds (1.38 angstrom). We also find that the effects of the layer stacking sequence such as AB or AA' is not significant. Fort the C(2)F (CF(0.5)) system, an earlier model in the literature indicated that all carbon atoms have only sp(3) hybridization due to coexistence of C-C and C-F covalent bonds. However, in this work, we propose a new C(2)F (CF(0.5)) crystal structure in which half of the carbon atoms, has sp(3) hybridization due to C-F covalent bonds and the other half has sp(2) hybridization as found in pristine graphite. Besides, with the structural models of graphite fluorides considered in this work, their formation mechanism is also clarified. Initially, two fluorines are positioned at adjacent carbon atoms with the trans geometry, and then one graphene layer is fully covered with fluorine while other layers are still pristine. After full coverage of the graphene layer, newly added fluorine will get located on this pristine graphene layer, and then, finally, all carbon layers are covered with fluorine leading to formation of C(1)F through further fluorination, which was demonstrated by an earlier experiment.