The notion of the dynamic flexibility factor of a pipe bend to be used in problems on the calculation of harmonic vibrations of pipelines is formulated. Based on the Vlasov semi-momentless theory, simplifying hypotheses are introduced that make it possible to reduce the problem statement to the solution of the quartic differential equation. Using the results of the dynamic analysis for toroidal shells, the procedure for taking into account the increased flexibility of pipe bends under dynamic loading has been developed. The expression for the flexibility factor is derived as a function of both the geometrical parameters of the bend and the vibration frequency. The efficiency of the derived expression for the flexibility factor is illustrated by a great number of examples.