Formation flying is regarded as a feasible solution to bring order of magnitude improvements is performance and capabilities of our space assets. To take full advantage of the benefits offered by formation flying concepts, it is necessary to develop and examine its dynamics models. In this paper, four models namely Perturbed Nonlinear Model, Unperturbed Nonlinear Model, Linear Elliptic Model and Linear Circular Model are studied. Also, an error index is given to measure accuracy of each model. Based on our simulation results, compared to Perturbed Nonlinear Model as the reference, minimum error index was observed in the Unperturbed Nonlinear Model. Due to linearization, the Linear Elliptic Model exhibits some error, as the formation size expands. Error index in the Linear Circular Model increases as the relative distance increases. Furthermore, its error index experiences rapid increase, even for small eccentricities. Considering the effects of these error sources on each model, one may be able to choose the appropriate model according to the desired accuracy for a given mission.