This paper presents two novel analytical wake models for crosswind kite power systems. One is developed based on the continuity equation, and the other is based on both the continuity and momentum equations. For each model, equations for the wake flow speed and the wake shape are obtained through a rigorous theoretical approach. Wake models for crosswind kites provide a first step in the understanding of the effects of kite-to-kite aerodynamic interactions on prospective wind energy kite farms. Despite a fair number of computational studies on these wakes, few studies have attempted to provide a concrete analytical solution. The primary motivation of this study comes from the fact that analytical models are simple in form and require very little computational power when being solved. The results from the two analytical models are compared with each other and are verified against computational results. Bearing several assumptions, these models are meant to simply offer a preliminary insight that will hopefully see many improvements with added complexity in the near future.