Free kicks are among the most interesting moments in a football match. The trajectory of a ball in the flight mostly depends on the way the ball is kicked. Especially fascinating is a phenomenon when the trajectory is being curved with respect to the initial direction of the shot, caused by the Magnus effect. Understanding the nature of the forces occuring on a ball in the flight is of a practical interest to both ball manufacturers and players. The goal of this thesis is to describe the motion of a soccer ball in a free kick, given an arbitrary impact on a ball. The geometry of the problem (including the modelling of a defensive wall) as well as different initial conditions and forces that act on a flying ball are elaborated in detail. The equations of motion are given by Newton's second law, comprise all the relevant forces on the ball and, given the initial conditions, are being solved numerically by the Runge-Kutta method of the 4th order. Solving the equations yields the desired trajectory of a ball. Different trajectories are shown graphically on a football field model. All the calculations and graphics are made in Python. A couple of different theoretical applications of the model are also shown. The final results match very well with the real-life expectations.