This paper presents a dynamic simulation of Unmanned Aerial Vehicle (UAV) moving on a launcher. The UAV launcher consists of a metal rail that is positioned at a launch angle, a spring and a winch to be able to stretch the spring. Prior to launch the spring is stretched into necessary tension and secured with safety pins, then released to launch the UAV. The influence of aerodynamic lift and drag forces on the mathematical model of a UAV will be considered in detail. Mathematical model a UAV moving on a launcher represented by differential equations are solved using a MATLAB software. The results of calculations are represented by a graph which shows distance, velocity and acceleration of a UAV while moving on a launcher as a function of time.