Analytical expressions, which connected of the unmanned aerial vehicle parameters and characteristics of landing's rope, are obtained. In particular, the relationship between the necessary length of rope and the value of its stretching during the landing of the unmanned aerial vehicle is determined. Meanwhile, additional dampers for the rope are not considered. The mathematical model of the deceleration process of unmanned aerial vehicle during its landing on rope is based on Hooke's law and Newton's 2nd law. One of the main assumptions at the development of the mathematical model is that of the braking of the unmanned aerial vehicle after its coupling with the rope occurs with constant acceleration.