Aeroelasticity is the science that deals with the elastic properties of a structure exposed to the flow of the surrounding fluid. The aircraft elastic wing structure can be described and examined by modal analysis. The results of modal analysis are natural frequencies and mode shapes. The natural frequency is a characteristic property of the structure in which vibrations of the largest possible amplitudes would occur by external excitation or by resonance. Such vibrations are harmful and sometimes lead to destruction. For this reason, natural frequencies need to be known. The paper describes the theory of free vibrations according to the theory of thin beams (Euler - Bernoulli theory). Euler-Bernoulli theory of thin beams is used solely for thin beams and for oscillation in only one degree of freedom. A computer model based on the mathematical formulation of the theory in the Python programming language was developed. The NACA4415 aerodynamic wing profile with the chord 1000 mm, with the length of the wing (cantilever beam) of 5000 mm, and the material of the wing/console Al6061. A theoretical and finite element method analysis of the cantilever beam and of the NACA4415 flying wing model was performed. Wing models with construction elements which can be found in the real aircraft wing were made in CATIA. The wings are made of stingers with circular-annular cross-sections, three different types of ribs (tip rib, normal rib and fuel tank rib) and a one-piece skin surrounding the previously described wing skeleton. The models differ in the thickness of the one-piece skin, but their external dimensions are the same. The wing wall thicknesses “s” are 8 mm, 10 mm, 12 mm, 14 mm and 16 mm. An analysis of the static strength of the wing with the smallest wall thickness (wing s8) and a modal analysis of all aforementioned models were made. The results of natural frequency vibration shapes and natural frequency values are presented and compared. The results show that the beam with right theory can be used instead of the complicated model, and that the Euler - Bernoulli theory provides approximate solutions to the numerical method for lower frequencies and for models with thicknesses at least 10 less than the length. Analysis of the influence of skin thickness on the characteristics of free vibrations suggests that, at small wall thicknesses, even twice as thick wall does not drastically reduce the magnitude of natural frequencies. In other words, with an increase in the wall thickness of the skin, the value of the natural frequencies cannot be drastically reduced.