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A perfect elastic cylindrical shell, subjected to a axial compression, with the lengthL, the radius of midsurface R and the thickness h, is analysed.The equations governing axial and transverse axisymmetrical motion of the cylindrical shell can be written as (а)Nx/(а)x =рh (а)2u/(а)t (1)D(а)a4w /(а)x4-(а)/(а)x{Nx(а)w/(а)x}+ Nθ/R+(а)2w/(а)t2=0 (2)In which x is the axial coordinate, the symbol t and p denote time and density of the cylindrical shell, Nx and Nθ are axial and circumferential membrane forces, u and w are the axial displacement and normal deflection of midsurface, respectively.