Airborne wind energy (AWE) is a new technology aiming at converting wind energy by flying crosswind patterns with a tethered aircraft. One of the main challenges of this technology is the launching and retrieving of the aircraft. A promising solution is the use of a vertical take-off and landing (VTOL) system in the form of multiple electrically driven rotors. Contrary to other approaches, such as a rotational and catapult assisted take-off, no detailed studies on a VTOL system for AWE have been conducted so far. The goal of this research is to investigate the opportunities and limitations of a VTOL system as a take-off system for a rigid-wing AWE system (AWES), by designing and simulating a VTOL system for the AP2, an AWES prototype of Ampyx Power B.V. The main research question to be answered by this research is how such a VTOL system can be designed. After having conducted a thorough state-of-the-art analysis (aka. literature study) the main research questions remain and are refined as: 1. What VTOL concept is most suitable for AWE applications? and 2. How do the aerodynamic forces of the AWES effect the VTOL system design? These are addressed and thoroughly analyzed in this report. The proposed and applied design methodology is based on the mass estimation of the VTOL system and its components: motors, battery and rotors. The sizing of the motors and battery is done by calculating the power and energy demand during take-off. Rotor mass is estimated using a statistical model. To calculate the required power, a blade element momentum model (BEM) combined with generalized momentum theory (MT) is used considering both inflow velocity and angle. A flight mechanics model is derived to calculate the required thrust and aircraft attitude. This model considers propulsion, gravity, and aerodynamic forces. A multi-disciplinary optimization (MDO) framework is developed to ensure consistency between the above-mentioned models and to calculate the minimum VTOL system mass for certain wind and operating conditions. A Simulink model of the VTOL system is developed using a multicopter flight path controller and a 2D dynamic model. This simulation model serves as a dynamic feasibility check on the VTOL system design and is used to iterate on assumptions taken in the design model. One of the main findings of this research is that by tilting the rotor depending on wind and flight conditions the minimum VTOL system mass is obtained. The VTOL system mass is estimated at 4.3 kg at wind speeds below 4 m/s and decreases to a mass of 2.1 kg at 10 m/s wind speed. However, for a fixed rotor tilt of -30 degrees (knee-sitter concept, newly introduced in this report), the VTOL system mass is only 100 grams higher for speeds between 5 and 10 m/s. Because a fixed rotor does not require any tilting mechanism, it can be concluded that this concept is most optimal in terms of mass for a direct take-off approach. For the tail-sitter and quad-plane concepts, the VTOL system mass increases with wind speed. A dynamic simulation has proved the feasibility of the sizing results for the tail-sitter, quad-plane and the new knee-sitter concept for a wind speed of 5 m/s and 10 m/s and a target elevation angle of 41.8 degrees. These simulations have shown that, under the assumptions of the simulation, the maximum motor power (from sizing model) is sufficient to successfully fulfill the take-off phase. It is found that the maximum motor power is only used to accelerate the rotor initially. It is not required in the transient flight phases. Furthermore, it is found that the additional power and energy, required for acceleration and transient phases is sufficiently low compared to the safety factor of 1.5 which has been taken into account in the preliminary sizing model.