On a typical 2D LEI kite profile, ow separation is expected to occur on both suction and pressure sides of the airfoil. This thesis is aimed to study various inviscid ow models that are capable of modeling such multiple ow separation phenomena. Inviscid models are capable of modeling single ow separation region over typical airfoils. In these models, the ow separation is modeled by releasing vorticity in to the ow from the separation location which are known prior and given as a direct input to the model. The separation locations can be taken either from experimental data or RANS simulation results of the airfoil. From the various singularity elements available for modeling, in this thesis point vortex elements and linear distribution of vorticity elements are utilized for modeling the ow and a step by step procedure of development of the solver starting from steady state to unsteady single wake and then to double wake model is followed. Each solver developed is validated against available analytical results. However, in the time line of the current study, the double wake model developed could not be validated with the chosen test case. The modeling challenges faced in the development phase of double wake model can be mainly attributed to the unclear modeling details in implementing the strength of the separation vortex that is shed from separation location. The other challenged include accumulation and crossing of shed wake elements through the airfoil surface, similar to the challenges reported by Rachel [25]. These challenges are clearly discussed and recommendations have been made for overcoming wake shedding problem. The author believes that such an inviscid model overcoming the modeling challenges experienced in double wake model, can be easily extended to model multiple separation regions over 2D LEI tube kites.