In view of the relevance of the problem of hydrogen embrittlement of oil and gas pipelines the problem of tube vibrations with weakened by hydrogen corrosion mechanical properties of the material is considered. The pipe is modeled by a circular cylindrical shell according to the classical Kirchhoff-Love theory. Weakening of the material is suggested to be taken into account by introducing the Young’s modulus averaged according to a certain law. Analysis of axisymmetric free harmonic vibrations of such a tube is carried out. The model is tested by the finite element method and is used further in the analysis of the effect of changing the character of vibrations of a shell with a mass belt. The formulas connecting the frequency shift with the parameters of the tube weakened by hydrogen corrosion have been obtained. They can be used in establishing the degree of pipe wear as function of time. On the other hand, the formulas make it possible to predict the frequency shift and, thus, to avoid the undesirable entering of the pipe to the mode with changing of vibration character which can be dangerous for its durability.