During their calendar life, passenger and transport aircraft run more than 200 thousand kilometers on the runways, which cause a significant part of the damage, both in the landing gears and in other units of the airframe. To reduce aircraft overloads at the stages of takeoff and landing (run-up and run on the runway) and taxiing, shock-absorbing struts with variable elastic-damping characteristics are used. Due to the fact that the parameters of the runway irregularities are in a wide range of values, it is necessary to use an adaptive system for controlling the stiffness coefficients and damping of the shock absorber strut, designed using an artificial neural network. The paper considered a network containing three layers. Using such a model, it is possible to implement an adaptive control circuit adjusting the elastic-damping parameters of the aircraft shock absorber struts to specific runway conditions (length and height of the irregularity, specific hardness of the runway). The velocity gradient method was used to train the artificial neural network. Half the square of the mismatch signal was used as the target criterion to be minimized. The calculated studies of the run up and run of the Il-114 aircraft on a dirt runway showed the possibility of reducing vertical overloads by up to 15% when equipped with a system controlling elastic-damping characteristics with a neural network. The comparison was carried out with an aircraft equipped with a “classical” (non-adaptive) system for controlling landing gear parameters.