The leading edge inflated (LEI) surf-kite is a suitable wing design for airborne wind energy (AWE) power generation because the bridling and leading edge design allow the wing to be de-powered while retaining good steer-ability. Fluid-Structure Interaction (FSI) modelling is required to capture the flight behavior of an LEI kite, due to it's extreme flexibility. Unfortunately, the current kite aerodynamic models do not meet the requirements for LEI-kite FSI modelling: they are either fast but insufficiently accurate, or accurate but computationally expensive. In particular, the current fast aerodynamic models are not able to represent the effects of the multiple flow separation regions - such as behind the LEI tube and above the canopy’s trailing edge - inherent to a LEI kite flying at a large range of angles of attack. This master’s thesis is intended to evaluate the hypothesis that a quasi-steady multiple-wake vortex lattice method can quickly and accurately model surf-kite aerodynamics to generate aerodynamic surface load distributions. This model uses multiple vortex lattices to represent the separation stream-surfaces in the flow, as well as the geometric surface itself. The vortex model chosen is the Vatistas Core Model, with a combined free- and fixed-wake wake deformation model. The method is applied to an arc-shaped wing with a Clark Y profile, a unity aspect ratio flat plate, and a demonstration LEI kite in order to assess the model's strengths and limitations. It appears that the usefulness of a multiple-wake vortex lattice method is strongly limited for membrane-wing kites, by an inability to enforce the Kutta condition on a reattachment-line when this reattachment-line crosses a separation-line. However, in certain high angle of attack cases, a single-wake and pressure-surface-separation double-wake vortex lattice method have the same order of uncertainty with respect to RANS results as is generated by the geometric approximations made in the TU Delft AWE group’s RANS studies of 3D LEI kites.