The disadvantage of the geometry of thin-walled parts, in terms of processing, is the low ability to resist static and dynamic loads. It is caused by the elastic deformation of elements with a low stiffness. Modelling approaches for the evaluation of deflections during machining are presented. Mathematical models of deflections, cutting forces and harmonic response are proposed. The processes of material removal and deflection of a thin-walled sample at the critical points are modelled. A frequency analysis was performed, consisting of a modal analysis of natural frequencies and a harmonic response analysis. As a result, a graph of the deflections amplitude from the frequency of driven harmonic oscillations is generated. The analysis of the obtained values was performed. As a result, the resonance frequency and maximum amplitude of oscillations for the operating parameters are determined.