Metallic bellows expansion joints are flexible elements in pipelines to absorb axial, lateral and angular displacements. Because of their shape and flexibility, they are susceptible to vibrations. Critical flow velocities are causing resonance effects which lead to failure in a very short time. There is the possibility of installing a so-called flow-liner into the bellows expansion joint to prevent this effect. However, this causes an undesirable increase in weight of the entire structure. The aim of this work is to clarify the question of whether and how these critical flow velocities can be described analytically. Due to its comprehensive assessment methodology, the German standard DIN 14917 serves as the basis for the calculations. For comparison, the EJMA guideline is also used. Approaches for calculating the critical flow velocities can be found in the relevant scientific literature. Along with the standard calculation these findings are implemented in a spreadsheet calculation using Microsoft Excel. Finite element calculations with the commercial code Abaqus show that the error in determining the spring rate is the most important influence factor for the accuracy of the frequency prediction. Methods for improving the accuracy by calibrating the calculations with experimental results are shown. An interface between Microsoft Excel and the DAKOTA optimization package is developed. With this interface it is possible to dimension a bellows expansion joint conforming to the standards and to optimize it for the occurring loads. Using this method, multiple scenarios are calculated in a very short time. This results in a significant time reduction of the design phase as well as in an improved design of bellows expansion joints.