The focus of this paper is the design of a pneumatic launch system (PLS) used for launching an unmanned aerial vehicle (UAV) and the verification of its mathematical model. Armed UAV systems without landing gears require a launch system for initiating the aircraft's takeoff phase. Existing solutions typically work on a mechanical or pneumatic principle. Within this research, a pneumatically operated system was chosen as they have been proven to be more reliable during exploitation. Many existing pneumatic solutions function on the principle of a piston pulling a carriage on which the UAV rests, whereas this PLS is designed to have the UAV itself act as a piston. The mathematical model of the PLS is based on the principle of conversion of the potential energy of a pressurized gas into kinetic energy. The verification of the device was executed using a replica of the UAV's fuselage which was equipped with an inertial measurement unit (IMU). After multiple launch sequences, the data was analyzed and the final velocity of the UAV was calculated. The results proved to be sufficient as they deviated with less than a 10% error compared to the theoretical values.